Most people here, I believe, will recommend using a MOS fet ex. IRF540
You will have to limit the current to 700ma with resistor unless that unit does this for you.
You're treating your LEDs like voltage-controlled devices, which they aren't. One fundamental thing most people (that are new to electronics) don't immediately realize is that an LED isn't a resistive device. When you approach its minimum working voltage, it turns from an open circuit into a dead short. So, meeting the voltage requirement of all 13 or however many LEDs means you will essentially be shorting the outputs of your supply. Don't do that.
You need a current-limited output. They make current driver ICs and turn-key power supplies for this. You just need to pick one that works for you.
Its a constant current driver, 700mA, so its fine to power the LEDs without a resistor,
whats not clear is if it can be PWM'd like this, but for simple on-off I think the TIP132
has enough voltage handling to spare (100V).
However its leakage current is woeful, 0.5mA, so it won't fully turn off the LEDs.
A MOSFET would be better, but a logic-level one, certainly NOT the IRF540,
and better go for at least 100V Vds to be absolutely safe.
I am a little worried that the constant current supply might not be designed with
load switching in mind though - PWM might not be advisable.
You should really use a relay on the AC inputs. That would protect your driver and prevent current wasted in the driver when not in use.
Beware that this driver is not dimmable. You can not PWM the transistor (mosfet); the spec sheet for the driver states that it has a 500ms set up time. That is typical for AC LED drivers.