Sounds like you have a Link 2000R not the less complex Link 2000. When you flip to BOTH you should see the voltages equalize, impossible for them no to. Check the current flowing into the start battery with a clamp meter after flipping to BOTH. If it is different than what the LINK is doing then the Link is likely bad. The Link 2000R (R=regulator) were buggy devices at best and is part of the reason no one makes that type of product any longer...

If you need an upgrade a Balmar MC-614 regulator with a Xantrex Echo Charger, Balmar Du to the start battery is a decent option alternatively a Blue Sea or Yandina combiner between the banks is also a good option.. You'd then need a new battery monitor and Victron BMV-600 would be good for the house bank..