Short life of LED parallel to Solenoid as indicator
The LED may already have a series resistor, the OP states that it is "rated" for 12V.  I suspect so because without current limiting an LED wouldn't last a second with 12V across it.  In that case it may be the inductive kick from the field collapsing during turn off that is avalanching the LED and causing the short life.

To "rectify" this put a regular diode across the solenoid coil so that it's reverse biased in normal operation and carries the inductive current when the solenoid turns off.

It should be rated for more than 12V (around 30V would be good) and for the same current as the solenoid.