AIR PUMP HTR, what is it?

I just checked the pump and it has only two leads for positive and negative. The harness it connects to is expecting 4 wires. I hope that confirms what you are thinking.

 

Yup your truck has a 2013+ harness and fuse box but the rest of the system is 2012 specs, not the first time I've seen that.
Manufacturers often do that on change years they start using next model year parts on the current model year, sometimes causes headaches getting the right parts.

 

yes that tells me your truck air pump doesn’t have the heater feature. Looks like they did all the electrical changes up to that point, maybe just the minor change of disabling a MIL associated with the heater relay circuit. I guess the bonus here is you could buy a replacement air pump from a newer Tacoma and it would work just fine.