The highest two gears (smallest two gogs in the back) are very slow to respond to the click on the shifter. It doesn't grind like it trying to shift - after 10 seconds or more it just shifts. And alas, this is an intermittent problem designed to make me irritable! Probably gunk somewhere that I can't see? Any suggestions?

could be anything. try this park tool guide first https://www.parktool.com/repair/readhowto.asp?id=64

You have too much friction somewhere -- the most likely culprit is the cable where it passes through housing. How old are the cables? Are the housings in good condition? Replace them with good quality cables and lined housing if you have any doubts -- these are not expensive parts and they are not expected to last forever.

Failing that, check the derailleur and shifters. If they're dirty clean them and lubricate them. If you still can't get it working take it to a shop.

When was the last time you cleaned your bike. There may be junk built up on the BB/cable guide/under the BB. Or lack of cable lubrication. Cable tension may be the culprit or the R/D hanger may be bent. The cable may need to be replaced.

There are several issues that may cause your shifting not to function properly.

Thanks for the good suggestions. I replaced the cables late last summer - so they have about 2000 miles on them. I'll give it a thorough cleaning and see if that resolves it.

But did you replace the cable housings? That is where most excess friction occurs, especially the short housing at the rear derailleur.
You could also try adjusting the shift cable with the barrel adjuster.
Failing that try hosing out the shifters with WD40.

Also, you might find a plastic screw head on your derailleur's inner arm that gives you two preload settings for the return spring.

Thanks guys!

Oh hey, I just realised the easiest way to increase return tension: thread a compression spring over the cable between the barrel adjuster and pinch bolt.

Prolly not the best way to do it, but you could give it a try with one or two of the springs you find in pushbutton pens.

Probably cable. Teflon coated cable + drop of oil=solution often. Else Sram used to make a "brassworm?" device for this.

Does it happen on the upshift or downshift? If it's on the upshift, it's probably a dirty cable issue. If on the downshift, you may need more tension. This assumes that everything was fine before and that you did not crash the bike. All the other suggestions apply as well, but these are the most common/easiest to check first, IME.

Thanks for the suggestions! A combination of cleaning & adjusting solved the issue.