2007 Chevy Express 1500 cargo van with 50,000 miles. Bought it used 5 years ago from dealer, was told it was from a fleet of Verizon work vans, so it sat idle a lot, thus the low miles. 

Problem started over 1 year ago and has remained the same since then (I dont drive everyday). No warning lights. When accelerating, just as transmission is getting ready to shift into the next gear, the battery power dips really low (but goes back to normal after shifting), the headlights and dash lights also dim and fade in and out when this happens, but it has never died on me and starts fine. Usually this lasts only 1 minute or less, then all returns to normal once my speed is stable. Happens around both 35 mph and 55 mph. I notice it more going up hills, perhaps it just lasts longer on hills because it takes longer to shift over.

Hope that made sense. I have had two different guys I go to for oil changes, check the battery and alternator and connections and they say it seems fine but I doubt they were thorough. Does this sound like a transmission issue or something else? I am not very knowledgeable about automobiles. Trustworthy mechanics are hard to find in the rural area I live in, so any help is greatly appreciated.

Thank you for spreading the good word and encouraging others to fix things themselves.