Yes, I think the switch was bad.
Actually there is no point in switching to 4WD without having the hub locked before. So the single H4 switch does it all together, in correct sequence and observing dependency.
For one exception: You need to be in 4WD quick and can't afford that procedure to fail. So it's a good idea to have parts of the procedure done before.
That's what the seperate switches combo does. You switch the hubs separately and get their proper engagement confirmed well before going into 4WD.
When needed, only the H4 switch to the tranny needs to work now, any time later.
You also have a better reporting: With separate switches / indicator lights, if so, you know where the issue is: Hubs or tranny.
The H4 button, though, still needs the logic to first 'read' that the hubs are locked.
If your H4 button causes a vehicle with separate switches not to go into 4WD, although the hubs are confirmed to be locked by that separate switch, this hubs-locked read contact in the H4 switch is faulty. Knowing that, you maybe can take a closer look and fix it.
A defective switch is, all in all, a rare case, I guess. In most cases the hubs or the tranny really don't engage due to electric failure on the hubs motors, or faulty vaccum operation on the tranny.
Thank you for sharing. This may help others.