How to reverse engineer controller outputs of a sprinkler control box?
Reverse Engineering 101


Look at return wire for ground switched solenoids from relays
measure DCR of solenoids for surge current rating (V/DCR)
use a dummy load  (Triac outputs will not conduct without a return load resistance or sufficient holding current flow.
map out continuity with ohmmeter to make a wiring table.


label everything instead of a schematic  e.g. P1-1 to J4-7



p.s.

The only questions in this bounty are : 


  Is there something I can use to 'watch' the connections? (Maybe cut the cable and add a circuit/monitor??) Is there a better method?


The board with 5 transistor switches and 7 screw terminals implies you have  5 outputs and 2 inputs for 24Vac power and return.

My assumption is you know how to use Ohm's Law and trace circuits and do design at this level. Otherwise, much to learn.

With a load, it is trivial to measure when power is switched on and locating the common screw voltage to which the power is connected to.

There is no need to cut cable and monitor current unless you wish to diagnose connection faults in the solenoid, then use an ommeter with power off.