Connecting the inputs will lead to the 2 MPPT controllers ( if that is what they are) trying to fight each other, leading to some oscillation in the chargers. Connecting the outputs leaving the input on the one open should do nothing, as the controller is generally expecting voltage on the output.
However the internal mechanisms of the controllers determines what they will do with commoned terminals, it really depends on the particular charger.
Simple non MPPT chargers you can connect in parallel, as the one with the highest float voltage on the bank determines the end of charge by dumping solar panel power, while the lowest battery hogs all the current till they all reach the same charge state with the same float voltage.