Do trim pumps have to be mounted up high for a reason or can they be relocated lower?

No. Don't need to be high for any reason. Any practical place where you wires and hydraulic lines will reach.

They should be at least as high as the trim cylnders. Preferably slightly higher to prevent the fluid from syphoning back down into the reservoir and possibly overflowing. Also they have a vented cap that would allow water into the reservoir if water somehow was to rise above the cap. The old style pumps where a sealed system but are harder to find now days.