Home Improvement → [HVAC] Bypass Humidifier - effective when just fan running?

Got an HVAC question that I just don't know the answer to...

I had a bypass humidifier installed on my furnace (forced air gas) a couple weeks ago...

GeneralAire 1042 humidifier - The way it's wired now, with a stand-alone 120-24v transformer, the solenoid opens whenever the humidistat calls for it, regardless of what the furnace is doing.

I run the fan all the time, so there is always air moving through the unit, I'm sure there's some benefit to the humidifier running when the heat isn't on - but is there enough benefit to justify the water usage; or would I be better to rewire it, so the humidifier only comes on when the furnace is firing?

There is a 24v HUM terminal on the furnace control board, that looks to only energize when there's a call for heat; so it would actually be bone simple to rearrange... But is it worth it?

Water is cheap, humidity is important.
I have noticed definite benefit to having the humidifier control the fan as opposed to just while calling for heat. If I only run it during call for heat the best I get is 35% on a ~30F day; running with fan brings it to 45%.

From what I've been told, if you run hot water through your humidifier it makes it much more effective when using just the fan - increases the rate of evaporation...

If the humidifier is near your hot water heater, that could be an easy fix