i agree that you probably have grounding issues. the suzuki variant chassis act super wierd when you
have a bad ground. the circuits back feed creating ground loops when they have to find their own path to ground.
you will have to start at the beginning and work to the end.
i start at the battery with the biggest grounding points - the battery post, the lug on the transmission, the ground wires to the inner fenders on both sides of the engine bay, the ground wire from near the distributor to the firewall, and on until i reach the rear lights.
i even add grounds to carefully chosen points. i use a common ground plate connected directly to the battery - post and run 8 gauge cables from that to those points on the inner fenders, the distributor mounting casting, and most of the additional powered systems i use for lighting and stereo.
i take every ground loose, clean the ring terminals with fine grit emery, clean the painted mounting points under the ring terminals, and use a stainless bolt or screw to replace oem hardware. every ground point also gets a little electrical grease to keep corrosion from re-occurring. i usually add a suitable internal star washer between the ring terminal and chassis metal.
the symptoms you describe indeed point to a weak electrical system and most probably grounds.