If I'm trying to get over my caffeine tolerance by abstaining from caffeine, what would be the more effective approach:

1) When I feel tired, try to resist going to sleep. This way, the body will get the message: better adapt to staying awake since that seems to be the general rule.

2) When I feel tired, sleep. This way, the body will get the message: better try to stay awake more since I seem to be sleeping way too much.

Or do neither have any effect on how quickly my tolerance goes down?

Find some decaf that you really like and switch to it, and keep the same hours you used to.  I had to do that 30 years ago due to a caffeine allergy that developed in my early 40's.  I had headaches for about two weeks, then was OK.  Now-- a nice cup of hot coffee (decaf) seems to be just as good a wake-up as caffeine was before.

1 hour ago, gib65 said:

If I'm trying to get over my caffeine tolerance by abstaining from caffeine, what would be the more effective approach: (snip)

2) When I feel tired, sleep. This way, the body will get the message: better try to stay awake more since I seem to be sleeping way too much.

^This one.

It may be difficult on whatever life schedule you have and try to keep, but if you sleep when you’re tired, then most other things tend to sort themselves out (including getting through the caffeine withdrawal more rapidly).

Add some ibuprofen for the headaches and drink lots of water to stay hydrated. These will minimize the negative effects of the shift. 

Edited December 10, 20178 yr by iNow

6 hours ago, gib65 said:

2) When I feel tired, sleep. This way, the body will get the message: better try to stay awake more since I seem to be sleeping way too much.

Allowing neurotransmitter pathways to work as intended without interference from caffeine would be the best option. Besides, just being well rested will reduce the need for drinking too much coffee and the problem will sort itself.

Drink decaffeinated coffee and be prepared for some headaches after about two weeks for a few days.

Thanks for all the feedback everyone. Sleep it is.