I'd point out that your understanding of what a VSR does is a bit off. It doesn't start charging the second battery after the first is fully charged. It connects the TWO BATTERIES IN PARALLEL when any charging source is detected. Some will detect charging sources one both sides, others will only work with charging sources on one side. Typically, all the charging sources are connected to the house bank side and the starting bank charges via the VSR paralleling the batteries.
Well, I didn't want to get into all the nitty-gritty details. My thought was that a small solar panel isn't likely to produce enough juice to get the voltage above the "cut-in" threshold until the first battery is pretty close to fully charged. Obviously, the larger the solar panel the easier it will for it to achieve that voltage. Also, as I recall, these relays need a minimum current to actuate the solenoid and put the batteries in parallel, so a little "trickle charger" solar panel might never get the circuit to close.