1. The relay shown is polarity sensitive (note the + on one side of the coil). The four diodes make sure positive voltage is supplied to the + side of the coil regardless of which incoming line has the positive voltage, and which is ground. In this example the incoming lines will be ground and 12 volts for moving the tab in one direction; the ground and 12 volts are reversed for moving the tab the other way. If you use a relay which is not polarity sensitive (coil doesn't care which end is + or -) then skip the diodes, just hook the incoming wires across the coil as well as to the normally open contacts. Note that the control lines must be 12 volts to run the relay; if you try to use lower voltages, to slow the motor speed, they may be too low to operate the relay. Likewise, if you use pulse width modulated (PWM) circuit for speed control the relay may not work properly.
2. The Trio uses PWM to control the trim speed. It must be "straight thru" to the motor. Do not use the Trio output to control a relay.
3. I have two trim switches in the cockpit, plus the Trio autotrim, so I built a relay logic deck to make sure no one control "fights" another. I use two DPDT relays for each cockpit switch (one for up, one for down). They're all in series, going thru the normally closed contacts. The Trio runs thru all of them. This way, you can apply less than 12 volts if you want the trim motor to run slower.
4. Safety: in case of a runaway trim I have the Trio and trim CB's side by side in front of me, so I can easily pull both of them.
5. As I'm sure you know, the Trio trim speed is pulse width modulated, and can be programmed to run more slowly at cruise speed and to run full speed at low air speeds. It also can be used manually even when the autopilot is not engaged. I have mine programmed to run very slowly at cruise speed, and I use it to fine tune the trim when hand flying the airplane.
6. The auto trim is most useful when changing airspeeds, e.g., letting the autopilot fly the climb, then level out to cruise. Or an approach. It is amazing for me to fly an ILS, starting from cruise, and ending up at 80 knots and partial flaps, and never having to touch the trim controls.