i agree with this quote. i just replaced the same "relay" in my 2006 odyssey that had 149000. my mechanic said it was a common failure. $6 at Oreilly's and it is guaranteed for life.Did you check the relay in the fuse box? From what I have read, the factory installed relay is subject to failure. Because my a/c was failing, I replaced mine ($7) and along with a system recharge, got me back up and cooling. See similar thread. But at 160k, anything is possible.
i would get on youtube and see if anyone else with an accord of similar year has made a video of it.
in my case i switched it out with a similar one (as instructed in the video) and i got ice cold air. so i swapped it back and headed to o’reillys. when i got there i took out the bad and it was hot....
i can't add the youtube link but here is the title of a generic honda one:
Honda A/C Fuse Relay Troubleshooting Problem and Solution