It depends on what you are trying to accomplish. If you are charging your batteries, I suspect that you are having an issue with your batteries. If that is the case, you need to disconnect the second battery and test each one to find out which one is bad if not both of them. If you are just really bored and feel like charging them for some reason, yes you can leave them connected together.
You can also get an air bubble under the ICP sensor which will cause havoc. I put my adrenaline pump in and ran it for about 5 minutes on high idle(1100 rpm) and then took it for a ride on the highway and pulled some wot runs on a long upgrade. Purred like a kitten by the time I got home. I also installed a new IPR and ICP when I installed the pump. The ICP was seeping through the connector and I figured if I was putting in a 600 dollar HPOP another 80 bucks for an IPR was worth not having the hassles. I also did a 300 mile trip one way the next day too so that probably worked out any other possible air issues.
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