The Oxford heated grips come with a “smart” Controller. If wired straight to the battery, they go into standby mode within 30 seconds of the ignition going off, not heating. After another couple of minutes they then shut off completely. Test yours to see if it’s doing that, if not you can reset them. I had to do that on mine after installation. Can’t remember which buttons to press to reset, google it.
I still didn’t trust then, so wired them through an ignition controlled circuit ( Bigpie's fuse box relay). The advantage of that is it cuts all power when you turn off ignition, but the “smartl controller remembers what setting they were on and brings them back on automatically when you restart the bike. I like that!