If you connect 12 V to the motor and the current drops to 0.13 mA, you can safely assume that you can leave that on all the time.
Have you looked at the circuit diagram of a car that already has the folding mirrors? If the left and right mirrors are in parallel, there has to be something to limit the power to whichever mirror gets to it's end of travel first. Once a device to do that has been designed, the manufacturers are likely to have used something that can limit the current for continually, and the reading of 1.3 mA seems to say that they have done that.
The timer relay you have shown appears to be one that cycles on and off. You want something different. You want a timer that runs briefly for one direction in response to an input, and then does nothing until the opposite direction is selected, when it should run in the other direction for a short time.
I think that you want two one-shot timers. Something like this:-
https://www.ebay.co.uk/itm/314160572814
You would need to connect +12 V to NO (normally open) on both timers, ground to NC (normally closed) on both timers. Put the door mirrors in parallel and connect them between the Common terminal on one time and the Common terminal on the other timer.
Connect +12 V to Vcc and ground to Gnd on both timers.
Two pushbutton switches, one for fold in and on for fold out, would go to the trigger inputs of the two timers.