Hmm, not enough. Should be a total of 13 zerks just on the front suspension, 4 on the outer A-arms, 2 on the trunnions, 2 on the upper ball joints, 4 on tie rod ends, and one on the idler arm.
Note that there are lots more points that should be lubricated : few drops of oil on the lower inner suspension pivots, top off the steering box, drop of oil under the ignition rotor, drop of oil in the generator rear bearing, repack the wheel bearings, oil the brake and clutch pivots, oil the rear springs, door hinges, top up rear shocks, just to name a few.
Personally, I like the grease zerks on the clutch shaft; the shafts without zerks wear out much faster. The later cars without the zerks also had different bushings with more surface area. I added the zerks when I converted my TR3A to a TR6 gearbox.
Also not mentioned (yet) are 3 zerks on the handbrake, and 2 on the rear wheel bearings.
Of course in all cases you have to be judicious about how much grease/oil you put in. Too much is almost as bad as none at all.
BTW, the workshop manual doesn't cover all of this. I suggest you find a copy of "Practical Hints for the Maintenance of the Triumph T.R.3", preferably 6th edition or later, which is the factory "owner's manual" for your car.
Also BTW, there were no TR3As built in 1962. Either the date has been changed, or your car is really a TR3B.