The right mouse button is pin 9. Both the E353 resistor (near the port) and C312 capacitor (directly reverse of Paula) are located on the reverse of the motherboard, so you'll have to take it apart. Unlike the joystick directional pins, the mouse pins don't go through the U34 encoder, so it's a pretty simple circuit.
I'm not quite sure how a bad cap or resister would cause the mouse button to always be on, since an open cap wouldn't matter as the mouse isn't sending power at all, and a short cap would short to ground. It's possible that somehow pin 7 (+5v) is shorting to pin 9, so check for corrosion around the mouse port and around the R953 resistors (near the C312 cap), as R953 is connected to +5v.
