Here is the simulation of the Beam-Beam (single tube) pulse, which is very close to the original. Rise time is almost identical to the original pulse, but fall time of the simulated guy is a bit grater than the original one.
So, for Beam-Beam trigger only we tried to apply different gates (different width w) and apply them with different delay Δ t. Then, we looked for the integral charged, collected within this gate. Main results you can see below:
Main conclusion from these pictures is, that for the gate of w=70nsec and gate delay Delta; t=40nsec we would really get 20% lost of signal intensity, as we suspected. So, for the future runs, one have to make sure, that triggers are properly aligned.