... "Eyes on the ball" is a good tip, an essential mantra if you will for beginner and intermediate players, since it helps you track and set-up for your shot... especially you said that you were playing with old-timers (like me *doh!*) where that phrase is often used and repeated... -However-, in themodern game, you will find the top players don't really track the ball all the time, at the level they play they don't have the luxury to 'watch the ball' all the time, instead, you will find that even before the ball leaves the opponent's side of the net, they will focus on the spot where the ball will land, and use peripheral vision instead to track the ball, which is something you can get from experience i.e. need to hear the shot leaving your oppo's racquet to judge how the ball is hit, and then judge where it will land (thereabouts)... so at a certain level, you can't really 'keep your eyes on the ball' anymore... you need to go to the next level...
...but having said that, Do watch the ball for now... get the basics right and when you need to go to the next level, it will become much easier ...for drills, just do the simple stuff i.e forehand/backhand down and cross courts initially slow then in increasing intensity to help you 'track' the flight... hope this helps!

hah hah... i used to have a lot of trouble when playing with older dudes too when i was *cough* young and learning... they just know how to control their shots and place it, thus negating our speed and power... heh heh, but that's something you have to learn to improve...

... i didn't have a coach too, in fact never had a coach until i was 18... so by that it wasn't about re-learning techniques... i wasn't to be bothered changing my admittedly unorthodox grip and strokes... what i did was look at pros on tv, but more effective would be to learn from someone you can play side-by-side or nearby with, so you can see better how he hits his strokes and footwork... i got my serve (version 4) from this guy (state player) in school and my backhand from a national player (his backhand was sweeeeeeet...)... so although it's an advantage to have a coach teach you, learning from your peers is an alternate way too...

This saccadic eye movement is used by elite athletes in many sports. Take a look at the work of Professor Joan Vickers, a Canadian scientist who has been studying gaze and attention of elite and amateur athletes for more than 2 decades. She has developed what she calls the "Quiet Eye" technique for training amateur athletes to use their eyes the way that elite athletes do. She has also trained Olympic and other elite athletes to improve these visual-mental skills.

Facing a 95 mph fastball, a professional baseball batter is unable to see (track) the ball when it gets to within 15 feet of him. The batter will track the ball from the pitcher's hand until it reaches the point where it exceeds his smooth pursuit tracking ablility. If he decided to swing at the ball, his head turn to the expected contact point and his eyes perform a "jump saccade". Just like Federer or Nadal, the pro batter keeps his head still and his eyes fixated on the contact zone. The head/eyes will stay "quiet" until the bat has swung thru.

Elite cricket players do an interesting variation of this. In cricket, the ball is pitched (bowled) in such a manner that it bounces before it reaches the batsman. The elite cricket batsman will track the ball as it leave the bowler's (pitcher's) hand. He will track it for a while in order to determine the bounce location. Before the ball gets to that bounce location, the batsman's eyes perform a jump saccade to the bounce point -- his eyes will "lie in wait" for the ball to bounce...

Tennis linespersons are trained to do the very same thing any time a ball appears to be headed toward their line of interest (like the baseline, for instance). The linesman will quickly turn their head and perform a saccade, fixating on the outside edge of the line -- "lying in wait" for the ball to come into their foveal (central) vision. If the linesperson is moving their head or moving their eyes as the ball is bouncing, their ability to accurately make a correct call is significantly hampered.

Back to the cricket batsman:

Once the pitched ball bounces, the batsman will once again resume a smooth pursuit of the ball for a short time in order to determine the contact point. He then performs a 2nd jump saccade to the expected contact point. His head & eyes remain "quiet", fixated on the contact zone, as he swings.

I have tried a similar sequence for tennis. I do not know if elite tennis players do this, but I suspect that many of them might do so for certain shots. I will sometimes try the "cricket" technique on serve returns. I track the ball from the server's racket until it gets to the net. At some point, before or after crossing the net, I perform a jump saccade to the expected bounce location -- "lying in wait" for the bounce. Upon seeing the bounce, my eyes resume a smooth pursuit of the ball until the ball gets too close to track. At that time, I perform another jump saccade to the expected contact zone, keeping my head very still -until my racket has nearly completed its forward swing.

The saccade, along with keeping your head still, will go a long way to making clean, consistent contacts. Moving the head, can throw off the swing path of your racket. The jump saccade is possibly responsible for being able to pick up the green/yellow blur of the ball after your smooth pursuit system can no longer track the ball.

Yes, the saccadic system should be used for volleys, in addition to keeping your head still. You would probably need to employ the jump saccade sooner on a volley than you would for a groundstroke near the baseline.

For a groundie, I can sometime smooth pursuit the ball all the way to within a few feet of contact. How soon the ball disappears, will be dependent on the speed of the incoming ball. A ball that travels from backcourt to backcourt will lose much of its speed due to air drag. It will also lose a significant amount of its speed on the bounce.

For a volley at the net, the ball loses less speed due to air drag because it does not travel as far. Because the ball does not bounce prior to the volley, no speed loss due to the court interaction occurs either. Therefore, on average, the ball will be traveling much faster for a volley than for a groundstroke. This means that you will not be able to smooth pursuit track the ball very long before it becomes "invisible". You will often nned to execute a saccade for a volley several yards/meters before the ball reaches you.