You are correct, I think anecdotal information is about all you are going to get. The amount of time from when electricity is applied until the motor comes to pressure has way too many variables to be explored in a general sense. You may be able to find some measured data on one particular motor/igniter combination but that would still have variables. Especially if different people install the igniters because placement can have a big affect on that time if it doesn't use a pellet like CTI.
Good luck
Thanks and, yep, many variables like propellant type, motor temperature, igniter type, voltage applied, current capability of ignition system, igniter placement, etc., etc. I'd appreciate anecdotal data from anyone, but I plan to gather data by using a single motor type and igniter type in a single stage configuration ignited by the staging system at first. Motor temperature will be held as constant as possible if there are major ambient temperature differences at launch times. I've built a 7.4V lipo powered MPU-6050 module/Trinket staging unit for delayed staging of 24mm composite motors, the staging delay(s) meant to keep max velocities low enough to use BT-55 paper tubing without shredding. Fin cans will be 3D printed, the 3D models created using an openSCAD fin can generator I've previously uploaded here (along with a number of other rocketry related openSCAD scripts I've written found in that ZIP file). I've made enough homebrew PCBs to make three of them, but plan to limit stages to three, requiring just two staging units (assuming everything goes well with two stages).