Rickenbacker pickups, despite being named "Hi Gain", are notably lower in output than may other pickups out there, so you're probably not imagining things. One common complaint is the volume of the neck pickup relative to the bridge pickup; I have a 2024 model and I noticed this on mine. You can boost the signal from your pickup by sticking a magnet on the back -
here's a post where I go into detail about doing that with some cheap neodymium magnets I got off Amazon.
Raising the pickups to be closer to the strings will also increase output, as the magnetic field gets stronger the closer you are. Don't get too close though, or the pull of the magnet can actually affect the vibration of the strings.
Both of these are relatively easy and cheap fixes to implement. You don't mention anything about your rig here, are you using any sort of preamp? If so, you can also use that to boost your signal.
Another thing to check if your bass is a 4003 with binding and dual outputs (not a 4003S) - which output are you plugging the cord into? The one closer to the neck that's labeled Ric-O-Sound is meant for a stereo cord, if you're plugging a normal guitar cable into that you're only getting one pickup. Plug into the rear output unless you are using the stereo output with the right kind of cable.
The cap is on the bridge pickup, and on newer models it's on a push/pull pot so you can just switch it off easily.