I have a 94 mitsu eclipse, I can plug a phone charger into my cigarett lighter and the light will come on but there is not enough power to charge the phone. I plug my emergency lights into another cars cigarett lighter and it worked, I plug them into mine and it would not power up where am I losing power? Or why? What can I try to fix this? I already tightened the lighter well and the power wires. What is left to try? Thank you for your time...
The Doughboy.

Try removing lighter fuse and cleaning contacts.

Also... At the center in the back of the socket is the power, 12V. The socket itself is the ground. The tab on the outside of your plug is contacting the ground.
Sometimes if you give the plug a gentle twist while inserted, you get things working better. My guess is you have a weak ground caused by wear, dirt, whatever.
If you use a cheap multimeter, it will tell you if your phone charger is seeing the full 12V it should.
Just be careful not to touch the power lead to the ground side while testing. Fuses short very easily and quick.