I think the contacts in your lighting switch are dirty. A similiar condition can occur with the shifter position switch in automatic CRXs. In cold weather, you shift into park, but the switch doesn't make contact for a while so you have to sit there and wait because the key interlock system won't let you turn the ignition completely off and remove the key. So, you can either remove the switch and try to clean it (I'm not sure how easy it is to disassemble the headlight switch), or simply replace it.
There are no headlight relays in US market CRXs. Canadian CRXs have a daytime running light relay, but full power and high beams are still controlled directly by the lighting switch, just as in the US market CRX.