This one has me stumped.
Here the situation.

15 amp circuit trips when heater plugged into it. Nothing else on circuit.
Ammeter reads 12.5 amps at breaker.
Same heater runs fine on an other circuit drawing same 12.5 amps

OK, bad breaker you say. Swapped breaker with one beside it in panel. Still trips.
Breaker is not hot. Takes about 5 minutes to trip.
Remove breaker and inspected bus. Looks perfect as does breaker contact.

What to check next?

Breaker panel is only about 15 years old FPE. I installed it and I also installed the circuit so I know where the cable runs exactly.

Don't bitch about FPE panel. We still install them new here in Canada. Very popular brand.

"Swapped breaker with one beside it in panel. Still trips."

My suggestion is to replace the breaker with a brand new one, instead of a used one that may or may not have the same problems.

By change the breaker that is tripping a gfci breaker? Another thing you can do is instead of clamping the load wire, clamp the main line. Does your meter have a max hold feature that changes only when the voltage increases?

Breaker is not GFCI or AFCI. I was clamped right at the breaker. I did use the hold feature and it did not spike high. The high max was 12.55 amps.

Do you think it is possible that more than one breaker could be tripping at the low value?

I guess a new breaker should be next try? Anything else that could possibly cause something like this?

Swap with the breaker you know it works on

Bad cable? Takes 5 minutes to trip,maybe that long to heat up the conductors and find a fault in the insulation.

I'm not surprised that two breakers, possibly from the same batch, both trip at the same value, and no one thinks that FPE has mastered the making of breakers.

Hmm, an FPE that trips early? I thought they usually had the opposite problem

Did you open and check the receptacle you originally had the heater plugged into?

The receptacle has been opened. What type of problem in a receptacle could make a breaker trip at 12.5 amps?

Trying to understand what other than the breaker could be the problem now that I have been think more about this.