To what terminal do I connect the T (brown) wire?
Am I right in thinking thinking the X2 wire from the baystat goes to the W2 connection.
I could probably use the correct wiring diagram to make this change.

Unfortunately, the color of the wiring is pretty much up to the person who installed it. Did you write down what wire went to what terminals on the old thermostat? Some old thermostats have wires that do not need to be used on some new ones. What kind of system is it connected to? Typically here are some of the terminal designations:

W - Heating (W1, W2 if it has single or dual stage heating)
R - High Side of the power transformer
Y - Cooling (again may have more than one Y)
G - Controls the Fan
O/B - Used for different things depending on system - could be a reversing valve or could put it into heating/cooling mode on older
C - Common wire from the transformer