If I was fitting that timer to make the installation the easiest and neatest I would drill 2 holes( the size of timer cables without the jacks )in the back of the switch cover at each end on the side where it transitions from flat to angled is (drilling from the inside of cover will stop drill bit skating around).
You need to solder the supply to timer to the red + and black - ,and UV negative is the yellow wire the IR negative is brown .
The only issue I see is if the timer you purchased is switching the positive wire then it will be of no use to you.
Easy way to check that is with a continuity tester ,test from negative into timer to negative from timer when no power applied and you should have an open circuit, if you dont do the same test on the positive in and positive out and see if positive is an open circuit. which ever is an open circuit is the one that is switched via the timer .
if it is switching the negative and positive at the same time ,don't worry about soldering the positive out of timer onto the switch its irrelevant ,we only need to switch the negative.
If you switch the positive and negative wire the spectrum you are switching will work but the other spectrum won't work .
I hope that makes sense.