How do I find the background noise level of my impulse response measurement?

First do the procedure explained above. Then set the time window to the last part of the impulse response, using the last 0.2 seconds of the impulse response should give a good result.

Since we assume that the impulse response has died out and we have only stationary noise in this last part of the impulse response, we must set the scope mode to Stationary signal to get the right result.