Little Blue “power indicator” light

[1010]

The shore power connection on our Cardinal has a cap which when closed covers the connection, when open and there is power a little blue light comes on indicating there is power. The blue light no longer lights up, and there is still power to the trailer. I figure the bulb is out and wondering if it is worth the effort and expense to replace the cap.
Another question, I use a 110 grounded adapter to a female 50 amp plug during storage. The female 50 amp plug will still turn even after tightening the collar snug. Still have power, thinking of replacing the adapter, as the 50 amp cord snugs up properly.
Thanks