Gas gets low and engine light goes on?

[50Traveler]

I am slowly tackling the various bugaboos in my car.  Latest question is what is the likely cause of the service engine light coming on/flashing once my tank gets to be about a quarter full?  Once I fill the tank it goes off.  

I also need to replace the front parking brake cable.  If anyone has hints to do that please share them with me.

 

Thank you,

J