Where can I get the wiring diagram for the Laing Autocirc? I want to wire in a momentary switch so that when I am ready to get in the shower I hit the switch and the pump runs until the water is warm and then turns off. That way I don't have to worry about having the electric water heater run all the time to keep the pipes warm or setting the timer at the strange times I take a shower.

If you have the same Autocirc product I have, then it cannot be taken apart. The timer seems to be connected and sealed together with the pump. If yours is different, answer back with the wires that you can see and we'll see if the timer can be by-passed.
http://waterheatertimer.org/Water-heater-recirculation-system.html

With the ordinary Grunfos-type pump that is not on a timer, you can add a switch and have the pump work on demand as you describe.

And they make a product that does the specific job you describe. It's called a Demand Pump. Link above shows two different types at page bottom.

I have not tested either Demand Pump shown. They operate on-demand ... when you activate the pump, the pump quickly brings water over from the hot water heater.

So the Demand Pump has a higher volume pump than the Autocirc or Grunfos.

I question a two things about the Demand Pump. 1) How will the increased pump pressure affect local pipes, especially supply tubes under a sink. 2) How HOT does the pump get? If pump gets hot, and it is located under bathroom sink next to paper goods, then that is a hazard. Some regional building codes don't allow ceiling light bulbs in closets because the bulbs get hot and start fires when people pack their closets full.

The Laing ACT-303-BTW does indeed come apart. The timer module can be pried out with a screwdriver or knife, and the main
electronics can be extracted from the body by removing 2 phillips screws.

I wish to wire the pump directly to line and control it from a wifi switch. The pump has 5 lines coming out: green, green, red, brown, black, yellow. Which 2 lines need to be attached to the power?