About 4 days ago, I did a routine oil change on my '05 3.0 and when I started it up afterwards my fuel gauge was on empty and my light was on. Thought it was weird but I disconnected my battery and after I reconnected it everything was fine. Now today, I get off work and sit on my phone for a minute with the truck on idle and I hear a gauge needle move. My fuel gauge needle had dropped to E and my light was on again. I work 2nd shift so it was around midnight and I knew I had 3/4 a tank left so I decided I'd deal with it in the morning but I noticed while I was leaving that both my headlights were super dim. I got home and disconnected my battery again and, once again, it "solved" my fuel gauge issue. Haven't had a chance to look at the headlights, I'm waiting until it isn't the middle of the night. Could these two issues be related in any way? I recently went and got my fuel pump replaced so I'm suspecting the gauge issue might be from there (floater perhaps?) but I figured I'd ask around.

Edit: It's worth noting that only the low beams were dim. Fogs and high beams worked fine.