Just turned on my Honeywell humidifier HE250A1005 and the water comes on and off every 2-3 minutes even if the furnace is not running.

SOURCE: Aprilaire 760 Humidifier water continues to run

You need to determine whether the problem is in the solenoid or in the furnace electronics. You could put a voltmeter on the solenoid connection to see if the furnace is still holding the solenoid open after the blower stops. This will tell you whether it is the solenoid or not.

SOURCE: Continous ware flow on Honeywell HE220A Humidifier

I am having the same problem. I have had my humidifier for about 5 years now and I just started having the problem where the water continuously flows through the solenoid. I took apart the solenoid by removing the fittings from both sides. When I did that, I noticed that there was a hole in the metal that allowed me to see through to the other side. Apparently, it had corroded and and broken through, allowing the water to pass through the solenoid without really going through the valve within the solenoid. There are several sites that sell replacements for about $70, which is not cheap, but cheaper than buing a new humidifier for $120. Here is one site I found: http://www.iaqsource.com/product.php/honeywell/32001639-002/?product=112783&category=1142

SOURCE: cleaning a furnace humidifier steel filter?

Most water panels are generally replaced once a year on flow through humidifiers.

SOURCE: Water keeps running to Honewell 360A Whole House Humidifier

You may need to replace the valve that is wired to the furnace that controls the water flow

SOURCE: Installing the Honeywell HE360A humidifier.

should be 2 wires going to humidifier you will connect wires from humidistat to them.