Odd electrical problem

I have a 98 century with an N14. There is a faint hum or buzz under the driver side Dash with the Ignition off and the tachometer will occasionally twitch. It’s like an ignition solenoid is Not killing the power when the key is off. I also have a crank but no start situation. Any ideas? Thanks for your help!

 

Also there are 9.9 V at the fuel shut off solenoid with the ignition key off. Brand new batteries. The noise behind the dash is more like static but it’s not an air leak there is no air pressure.

 

I think I figured it out. There’s a starter solenoid on the firewall. It had continuity between the big posts with the batteries disconnected. I think it was the original from 1998 because the posts broke off when I went to remove the nuts.

 

Well I replaced the ignition solenoid and that didn’t fix it. I still have 9 1/2 V at the fuel shut off solenoid with the key off. The gauges still twitch and the static sound is still present behind the dash. Does anyone have any ideas?

 

Thank you so much for your help! I tried both and nothing changed.I’m not sure if it’s related to the new batteries I just swapped in but the dash says no data link activity.