Can I use more than one antenna with a radio module (say rfm69) and switch between those antennas electronically, say by a transistor
Forget RSSI, I don't know why anyone thinks it is a sane idea for this sort of thing, but it keeps coming up. 

Instead, use 4 aerials, an FM receiver module and 4 pin diode switches (Or the equivalent packaged up by someone like skyworks), you drive the switches in quadrature and thereby cause the effective antenna position to move in a circle, this produces Doppler shift which the FM recever demodulates as a sine wave, the phase between the recovered sine and the antenna switch drive gives you bearing. 

This is sensitive to multipath, but much less so then RSSI based sillyness.