Codes P1285 and P1299, where is the cylinder head temperature sensor located?

The CHT is on the rear of the LH cylinder head, just above the bellhousing. The codes you have suggest a wiring problem at the sensor. An unplugged or broken wire to the sensor will trigger both codes. I have seen them chewed off by rodents but the common issue is if the harness is pulled up so it creates a hard bend.

If you replaced the sensor but still have the temp gauge issue, then it's time to check the wiring itself. A broken wire to the sensor will act the same way as a bad sensor. The easiest way to verify the wiring would be to use a meter and test the resistance between the two ends on the wires for each terminal. So, you would unplug the CHT then go to the PCM at the firewall and find the yellow wire with green trace at pin 41 and use the probes at both ends. You want to see as close to zero ohms or a beep if you have a continuity tester. Then do the same with the gray wire with red stripe at the CHT conn and terminal 58 on the PCM. I suspect it will be the first wire. To repair it will either be replacing the connector end or running an overlay wire if it's not a bad connector.

https://www.2carpros.com/articles/how-to-use-a-voltmeter
https://www.2carpros.com/articles/how-to-check-wiring

Good to hear, usually the thermostat would set a different code or actually show as the engine overheating.