Here's what my current loadout consists of:
Mad Bomber Helm
Mad Bomber Suit
Aegis/Crest of Almire
Nitronome
Volcanic Pepperbox
Elite Boom Module
.
.
I'm wondering what I should get for my second trinket slot? I'm thinking either a Heart Pendant (because more health is always good) or a Trinket to improve my gun (in which case would it benefit more from +Speed or +Damage?)
In the clockworks (with that loadout, I bet you are not doing PvP), a heart pendant is unsignificant. With a +12/+15 vitapod on top of your current health, it's not going to make a big difference. And if you went so far with that loadout, you probably don't need it.
I would go with a trinket for your gun. For autoguns, the charge is very popular, because it does so much damage. If you use the charge, definitely go for CTR.
If you don't, do you find yourself wishing that you could shield cancel just a little faster ? If so, get ASI, that's what it is really useful for. If, on contrary, you just want more damage, just go for DMG.