So far I was not really interested to reproduce this temporary faster blinking rate. But now I got curious if I can do it with some minimal components that will still fit in the control box.
So as far as I can tell when watching the cave scene - it blinks faster for a second or so when it is powered on and then slows down to the normal rate. Same happens when led colors are switched - when the red led turns on it first blinks little faster and slows down and then when it goes back to green - again it blinks faster for a short period and then slows down. Finally, it looks like when he clicks or touches with the tool whatever changes the led to red - he keeps the tool pressed all the time, so the rate slows down on it's own.
I choose this time to play with the control pin to vary the speed, but the same approach can be used to run in parallel to the timing resistor R2 or to the power supply like in my previous test.
So as fist step I wanted to make it start faster when powered on, but then slow down on its own after a while. From what I understood by playing with the control pin you can only slow the rate but cannot make it faster than what is setup by R2 and C1 pair. So in this case R2 and C1 should be selected to blink at the faster rate and then use the pin to slow it down to the "normal" rate.
This is what I came up with :
So what's added is the resistor R4 connected between pin 5 and + and the value is selected so when connected it slows down the rate to what looks good. Then there's a transistor that acts as a gate and essentially connects R4 to +. However this is delayed a little until C2 is charged enough. In summary: C1 and R2 set the fast rate; R4 the slow rate; R3 and C2 the time from power on until the rate slows down. R5 is there just so C2 has some way to discharge when the power is off (otherwise the whole thing will work only the fist time it powers on).
Then I started looking how to speed up when by pressing a momentary switch and then slow down when it is released. This pressed together with another momentary switch that swaps the leds (or maybe using a single dpdt switch) will get pretty close to what is seen on screen (but not perfect).
Here is what looks with the switch:
It just shorts C2 to ground to drain it instantly and maybe is not the most elegant way to do it but it worked. I prototyped it on the breadboard and tried to record a video, but my phone camera is messed up and hunts for focus all the time so it turned out pretty annoying to look at. But if anyone is interested I can share it. I didn't try to fit this in the control box, but I think it should still fit (if the battery is external though).
So the only problem with this is if you press the two switches together (the one to change the color and the one to change the rate) and keep them pushed like it is in the cave scene - the red led will start at faster rate but will not slow down. Then when you release - the green will start at the fast rate but then slow down as desired.
In my own build I don't use a switch for changing the color but just short 2 traces with the tool, so placing a switch below that will probably allow me to press on the traces and pushing the switch at the same time - then slide the tool a little so it is not shorting the traces anymore but still presses the switch, then slide it back over the trace then release to get both the color and the rate change as in the movie - but is far from perfect solution.
I think if one of those switches that are open on one side and closed on the other is used can make this work better but I don't have one to try.
But my idea is to add another pair of resistor and capacitor R6 and C3 (same values as R5 and C2) and use the switch to toggle between the pairs. This way when you press the switch the loaded capacitor will be replaced with empty one so the rate will speed up; then slow down again when the empty capacitor is charged enough - while you still hold the switch pressed (meanwhile the disconnected loaded capacitor will discharge through its resistor). Then when the switch is released the capacitors again will be swapped and the whole thing will repeat.
Something like this:
I've not tried this though as I didn't have the extra components needed. And I don't think I can fit all of it in the control box if I have to, but in my FX build I can move some of it into the main body where I have plenty of space.