Here's a thought. The AirForce One system we use has a LED light that is placed on the dash board and illuminates when vehicle brakes are applied. You monitor it via your back up camera. It was hard to see so I fabricated a larger, brighter one using a red LED light bar I bought at a RV show. I mounted it on a pad cut from a cheap door mat from HD. It has a two prong plug so it can eaasily disconnected and stowed. You can splice into your brake light wiring and accomplish the same thing for around $20 total.
2014 Keystone Bullet 22RBPR
2005 GMC Envoy Denali