I've been having trouble recently with my brifters. Whenever I apply the brakes I feel that there's a bit of gap that feels like the brake cable is loose. I checked that the brake cable is tightened but I'm not sure if the the brakes still need adjustment. I'm guessing the problem is either with the cable, the brakes need adjustment, or the brakes are dirty.. I also lubricated the cable and the brake's pivot points but that didn't solve the problem.

That sounds like it could be friction in the cable or the brake pivot, but seeing as you lubricated the brake, it's more likely to be the cable. What did you lubricate it with?

Also, are they dual-pivot brakes, or single-pivot?

I used Triflow TriFlow Superior Lube.

I played with the bolts on the brakes and it helped a little but I'm not sure how to fix it completely. Every time I apply the brakes and let go, there is always a bit of space left to push down on the brakes (literally) to retract it back to it's "normal open" position.

I don't know about the brakes but I have a pic.

+1

Sounds like there is excess friction in the cable housing - it is a common occurrence. Simply whip the cable out, check for corrosion and either re-lube and reinstall or just replace for a new one. It is unlikely that the housing will need to be replaced too, but it might, so just see how bad the cable corrosion is.

+1 for cables as the culprit. Look for a kink in the cable, or too much/too little bend in the housing at some point, or possibly the ends of the brake cable housing weren't trimmed cleanly and the metal winding inside the cable housing is grabbing the cable.

BL

+3 for the cables. From the looks of your photo you can see that the cable has a slight bend in it which would suggest that the brake calipers are returning properly but the cable is stuck somewhere.

I only looked at part of the rear brake cable and did not see the front and the part where the handlebar tape is covering. Is unwrapping the handlebar tape the only way to expose the remaining cable?

OK. Open the brake QR. If you can squeeze the brake calipers shut with your hand ( not by pulling the lever) and they pop right back open, then you can rule out the caliper.

If it's rear brake and there is exposed cable, pull on the cable mid span. If the brake pops right back open, your trouble is between there and the lever.