Malaysia (Time to process: 20 minutes)
Immigration booth first, then, over on the left, there is a cabin with "customs" marked on it.
Take your Carnet in there and have a cup of tea.
Friendly smiles all around, then drive off.
Simpler than falling off a plank.
Thailand (Time to process: 30 minutes)
Immigration at one of the booths first.
Quite inefficiently, there is only one kiosk handling vehicle documents, even though there four doing the immigration controls. Exit from the immigration booths, merge into the common exit lane, and then park at the end, still under the compound's canopy.
The customs kiosk is next to the last (Thai-side) immigration kiosk.
Present your carnet at this office, and details are put into the computer. At the next window, the Carnet is completed, and you receive a computer printout, which is the Thai equivalent of the Carnet document.
Treat the printout as you would your Carnet. Look after it well. Take it out for meals. Read it bedtime stories. Let it choose what to watch on TV occasionally. Because if it gets a grump on, or walks off in a huff, you have a problem.
There is another drive-through customs check about 1km up the road into Thailand. Here they check your paperwork again.
With regard to insurance documents, I offered my docs with my Carnet, passport, etc. I'm therefore uncertain whether the insurance was checked. I think it may have been. You need it anyway, so obtain it before entry into Thailand.