Budget action cam with remote start/stop?
 

I'm not much of one for taking videos, but I've got an old HD gopro clone that works well for me (along with mounts etc) ... but I'd like to be able to start/stop recording by remote without interrupting my riding. Some sort of image stabilization would be good too, but isn't essential.

Is there anything that does that without breaking the bank?

Easy answer is always "someone else's gopro that they used twice and has been gathering dust". My old gopro 3 came with a remote control, and I am sure the newer ones are compatible too. Look on Facebook Marketplace etc.

That said, remember that any device that can be turned on by remote, is by definition not fully off in that mode - its wifi chip will be working to receive the remote's signal - and it WILL drain the battery. So it's not a "leave it on the bike until I need it" thing, it's more of a "turn it off on the boring bit to preserve the battery a little" thing.

Having messed around with gopros for a while, I am very happy to have switched to a permanently mounted moto dashcam. Has a wired remote to start/stop, runs off the bike's charging system, starts recording whenever I turn on the ignition. Front and back 1080p cameras, no image stabilization, but cost me $250 - half the price of the newest gopro.

Another vote for used GoPro. Every time they bring out new one you can score last years model for less money.
DJI is also an option. They've made good action cameras. I especially like the ones with the swivel head (gimbal).
Older smartphone is can be a good choice. Install camera app that you can start from another phone using WiFi.

Thanks for the tips! This will be chest mounted (bike mounted hasn't worked so well for me before) ... I'm not as worried about battery life, it's more a case that I don't want to sift through a lot of footage - like I said I'm not much of a videographer, but it would be nice to grab a minute here or there for my own memory :)

Old GoPros capturing in HD quality have perfectly good enough for most of my needs, but controlling them on the move, where there's only you and you want to switch them on and off as you ride is not easy. I have the official GoPro remote but that's not a lot more usable as it still requires you to fiddle with it. A simple handlebar switch - like repurposing the horn button for example - would be much better but the only stuff like that I've seen (for motorsport use) is crazily expensive.

I have a couple of old Hero 4's that still work well - or they did until last summer when one of them suddenly stopped recording video when the bike was moving. It was fine when the bike was stationary, or if I was taking a still image but not when I was riding. I tried two other cards with the same result so my guess was some sort of vibration issue. Both of them were hard mounted on the bike so that may be the problem and a chest or helmet mount wouldn't suffer from that. You live and learn but it was disappointing to come back with little footage. I'll be putting a lot more testing effort in before next year's 'adventure'.