Raspberry Pi GPIO Configuration - Burnt out I/O?

I have two inputs from magnetic contacts wired into my PI. One works and the other doesn’t. I’m not sure why.

binary_sensor:
  - platform: rpi_gpio
    ports:
      16: Driveway Gate Closed Limit
    invert_logic: true
    pull_mode: UP   
  - platform: rpi_gpio
    ports:
      13:  Garage Door Closed Limit
    invert_logic:  false
    pull_mode: UP   

I have zero problems with the driveway gate. It’s worked well for months to years now.

The garage door is another issue. I tried pull_mode: DOWN and tied this magnetic reed switch between GPIO13 and 3.3V. It worked for a while. Then, it got flakey (rapid fluctuations) and finally quit working altogether. It lasted a few days, at most.

I then changed to pull_mode: UP and inserted a relay into the picture. I tied the contact to GPIO13 and GND to the relay contacts. Again, it lasted only a few days and then stopped working.

Now, no matter what I configure and what I do with GPIO13, it no longer seems to work. I can’t figure out what I’ve done wrong here. Should I have inserted a resistor or two, maybe?

Using mostly Cat6 (existing infrastructure) between the RPI and the magnetic reed switches. Driveway gate is maybe 25’ and the garage door is maybe 100’.