Would this be the pin 4 (which I’ve highlighted in red in my image?) this is assuming the connectors are the same, sorry I don’t have an OLED handy currently.
Apologies, but this image is pretty much as far as I took my analysis of the joycon circuitry (on a regular Switch rev board) … I may have went slightly further in my analysis on another topic somewhere on the forum 
even though this is a regular rev, the circuit (even if using different IC’s) is most likely going to be very similar on OLED
Take this with a pinch of salt, as I didn’t take the time to positively ID a lot of the components in the area (or can’t remember if I have done prior), but off the cuff, it looks like the 6-pin IC you can see on the left is potentially a mosfet, and the 5V output is likely “switched” via this, if that or any of it’s surrounding components were bad then this could potentially cause the issue. (which would explain why one joycon side doesn’t have the issue if there is a separate fet per side)
Again, pinch of salt, may not even be a mosfet, may not be switching the output etc 
Regardless, might be worthwhile disconnecting battery and measuring resistance on pin 4 of the connecter relative to ground and ensure pin is not being pulled low (for some reason) and if the IC I identified is a mosfet, identify it’s gate and see if it’s high (assuming n channel) and if not, why not.
To find the potential mosfet, buzz out in continuity from the pin of JC connector on any of the IC’s in the most make sense areas