Taking the questions in order. Replacing both shoulders in one sitting is rarely done, and the reason is practical rather than surgical: after the operation the arm rests in a sling for about 2 to 6 weeks, and a patient needs one functioning arm to manage washing, dressing, eating and getting in and out of a chair safely during that period. Two slings at once is a very hard recovery to run at home, so the overwhelming majority of bilateral cases are staged, meaning done as two separate operations.
On the gap, there is no fixed rule, and what surgeons generally wait for is the first shoulder to be genuinely useful: pain settled, out of the sling, driving again at around 6 weeks, and a good way into its physiotherapy, so that it can carry the load while the second side recovers. In practice that usually means at least 3 to 6 months between operations, and many people leave it longer because the second shoulder does not need doing yet. A shoulder keeps gaining strength and movement over 6 to 12 months, so at six months yours is well into that curve without having finished it. keencaravanner's two years is a common sort of interval; six months is at the shorter end but not unusual where the second side is already painful.
Your surgeon's comment about the cuff is the important one. The two sides are assessed independently, and it is the state of the rotator cuff on each side, not the fact that the first was a total, that decides the operation. A working cuff points to an anatomic total; a torn, irreparable cuff with arthritis points to a reverse, where the deltoid lifts the arm instead. It is entirely ordinary for a person to end up with one of each, exactly as keencaravanner describes, and the fork is set out plainly in an anatomic versus a reverse shoulder replacement. A reverse has a somewhat higher complication rate and tends to leave more limit on reaching behind the back, so if that is where the left is heading it is worth understanding before you decide, not after.
As to age, the sums for a second shoulder at 80 are the same sums as for the first: fitness for a general anaesthetic, which is reassessed rather than assumed from last time, and the pain and function on that side against the recovery it asks of you. Age on its own does not rule it out, and the question of timing is covered in shoulder replacement at what age. Whether your left cuff is repairable, which operation it points to, and when your right is ready to be the only arm for a few weeks are all judgements for the surgeon who has your imaging and can examine both shoulders, and I would put those three questions to him directly.