2013 Prius "Start" button light won't turn green/car won't start intermittently

When I typically press the brake pedal, start button shows a green light and allows me to start the car when I push the button.

1. I've recently had some intermittent issues where the "Start" button won't turn green and stays off even when I depress the brake pedal.
   
   
2. After the third time I depress the brake, the Start button light will turn green, but I still won't be able to start the car - however, I'll hear a slight struggling 'whirring' noise unlike the one you usually hear. Brake can become a little stiff during this time.
   
   
3. After depressing the brake pedal a fourth time, the light will not only turn green but I'll be able to start the car and run without issues.
   
   
4. I wondered if it could be a brake light switch contact issue - however, one thing I noticed when I tried turning the Prius to accessory mode to do a 12v battery check was that the car was unable to turn to accessory mode (which does NOT require the brake pedal depress). After multiple button presses/brake pedal taps, the car started whirring a bit and was finally able to start up, after which I checked the 12v battery was at 12.2V when car was off/14V+ when car was running.

This issue has come and gone randomly for a couple of months now, and always seems to go away after multiple attempts at the brake pedal - any idea why this is happening?

Can brake switch light be an issue if the Prius cant even turn to accessory mode? And what could cause the Prius to not be able to switch to accessory mode if the 12v battery health check seems to be OK?

Key fob battery is brand new so not key fob issue.

 

Battery is likely 7-8 years old. I’m just confused as I would assume the car would just refuse to start altogether in case the battery was dead/dying, versus always being able to kick back up after trying to depress the brake pedal 3-4 times.