Prototype is done. And it works!!!!
Who'd have thought right? I also managed to get that tiny component on a perfboard.
A few notes if anyone is looking at this to build their own circuit:
Remember Vth_on is critical for timing in this circuit. I ended up with a MOSFET which had a threshold voltage of 1.4V. With the resistor at 10meg the resulting circuit took closer to 15min to turn off the red-dot finder. I replaced the 10meg resistor with a 1meg resistor and I happily hit almost 60 seconds of light exactly before the laser turned itself off.
Also I've decided against a fancy case. My first iteration of the circuit ended up being smaller than the brightness control of the red-dot finder, so I'm doing what any enterprising hacker would and just building the circuit directly into the red-dot finder.
Now the obvious question to all of you:
If I build like 20 of these would you prefer a stand alone circuit with battery holder that has simply two connections which can be connected to the battery terminals in the red dot finder (i.e no opening the finder, no voiding warranties if you care for that sort of stuff). This would look like the earlier rendering I published above.
OR
Would you prefer a cricuit as tiny as humanly possible integrated in the back of the pushbutton which could then be fitted to the finder with careful application of a hacksaw and some glue? Oh and there's 4 wires to solder with this method. This would look like the rendering below.