OK, it's not a GoPro, but it is a clone action cam. B&H has a Deal Zone 1-day deal on a Sunpak 4K action cam for only 25 buck, with free shipping (US only, sorry non-US people).

I don't know how good this one is, but it is dirt cheap and discounted 58%. It has a display and WiFi connectivity, and a standard GoPro form factor.

I buy a lot of things from B&H and especially their Deal Zone deals. Some are fantastic discounts. If you've been wanting an action cam this is so cheap it's probably worth a try.

https://www.bhphotovideo.com/c/product/1626703-REG/sunpak_sp_4k_ac_kit_4k_action_9_piece_camera.html

 

I should also point out that B&H is a very reputable dealer and they take returns without trouble.

 

I picked up a compatible one some time ago, there was a deal at the time you got 3 micro memory cards with it, so turned out not bad, price wise.

 

@Yaakov
This made me think. What’s the smallest WiFi or SD card camera that you’re aware of? I’m looking for one with a width of 7/8” or less, and a length of ~3”. Height is irrelevant. HD is not a requirement and 720p is sufficient. I’ve started to look, but if you can point me in a direction, I’d appreciate it.

 

Most of the GoPro is case. The actual camera that my son uses on his quadcopter is pretty small. Less than the size of an electret mic capsule. Look into the ones used for the RC stuff.

 

@Yaakov
This made me think. What’s the smallest WiFi or SD card camera that you’re aware of? I’m looking for one with a width of 7/8” or less, and a length of ~3”. Height is irrelevant. HD is not a requirement and 720p is sufficient. I’ve started to look, but if you can point me in a direction, I’d appreciate it.

What is the nearest focus you need? What field of view? Are you taking stills?