Furnace keeps kicking off and on

I just yesterday dealt with one like that. It had electric ignition (glowing ignitor) and a single yelloow "flame sense" wire. This is only the second one of these I've found in a decade, but the problem and the solution is the same. IF your unit uses ion flame detection, the burner ground has become oxidized. It may look like metal against metal, but a fine coat of invisible oxidation had formed between the metal parts. It needs a good "ground reference" before it can detect the ions.

To fix this, I removed the burner. While I had it out, I scraped the flame rod tip some but it wasn't really dirty. When I put it back in, I intentionally made one of the self-tapping sheet metal screws dig a new groove instead of putting it back in the first grooves. I also got it good and tight.

Just as in the first case, the mere act of disturbing the mechanical assembly caused a better ground to be formed. It must be working, because I didn't have to get up last night and go fix it.

Probably. You'd have to inquire of the furnace maker if it is or is not. Speculating, since we have no information about what make or model furnace you have, it probably runs the burner until the heat exchanger is too hot, shuts off the burner until it's too cold, and starts it again. Very few furnaces have any ability to modulate the flame, so it's either on or off. In all likelihood the on/off time varies with the return air temperature (and thus, the heat load.)

The post-burn run to cool the heat exchanger after the call for heat is satisfied is certainly standard.