06 tacoma trd truck starting issues

I recently bought an 06 tacoma trd truck quadcab, and it runs fine except when a few days ago, when I started the car after 15 minutes, it wouldn't start again. Now it's more consistently doing the same thing. I don't know if I am correctly describing this, but it's on and off. I will try to upload a video with the sound when I try to turn it on. I checked teh battery voltage and it read 12.5 cold, then 13.5 after it starts. Please give me advice on what to check so I know what to do.

Thanks

 

Maybe you need a new fuel pump? How many miles on the truck?

 

108,000 miles

 

So I cleaned the terminals, and did the alternator test. I removed the positive with the truck running and waited around 5 minutes. As I was doing that, it was losing power and my lights will go dim unless I revved up the engine, where it would momentarily regain some light. When I checked voltage meter, it was at 12 and lower with my lights running around 11.8. So is it safe to assume that it is the alternator that went bad?

 

i have a 06 tacoma as well and reading your orignal post my truck does the same thing and idk what to do to fix it

 

Yea, I'm going to do a load test next to make sure it's not my battery and that one of my cells isn't bad, but we shall see.