You can prop it up with a capacitor. Much like the kiddies do with "bang caps" for their crazy car stereos, you can use something much smaller. A diode in the supply wire, followed by a small resistor, like 1 ohm, followed by a big capacitor would help with this. The diode is a one way valve that means the capacitor only props up the voltage on the GPS, not everything else.
It will keep the GPS alive for the time when the trim motor starts and hogs all the current, browning out the GPS. I can elaborate with a sketch and part numbers if you want.
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