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.
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