HOU Controller described possible runway incursion event when failing to properly identify a landing runway during parallel operations; the crossing traffic causing an ASDE-X alarm; apparently across the hold lines but still clear of the runway edge.

Narrative

I was working Ground Control when Aircraft X called off the runway wanting to taxi to parking. I instructed the aircraft to turn right on Taxiway C and turn right on Taxiway L hold short of Runway 12L. I also had a B737 holding short of Runway 12R on Taxiway H to cross 12R and 12L. I was also taxiing other aircraft around the airport. We have a lot of closed taxiways and runways at HOU due to construction and with the new taxi rules; I was really having to over focus on aircraft approaching closed runways so I could cross them without them waiting to long; it was also a lot of extra verbiage and made my session more complex then it needed to be. I was in position for about an hour when the event happened. With all of the closed runways and taxiways; and the bad weather and new taxi rules; I was feeling a little fatigued. I also had been training for the past month and not getting any good pro time. When I ask Local Control for the crossings for the B737 and Aircraft X; Local had an aircraft on final for what I thought was Runway 12R so I ask local; ' After Aircraft Y cross Lima West and Hotel East'; Local approved my crossing so I told Aircraft X to cross Runway 12L hold short of Runway 12R. Once I unkeyed; I realized Aircraft Y was touching down on Runway 12L not 12R; so I waited for the pilot to stop speaking and told the aircraft to stop. The aircraft stopped short of the runway but the ASDE-X sounded off. I couldn't see if the aircraft was over the hold line or not; but the Supervisor said it was; however it was short of the runway and the aircraft that landed was slowing. The parallel runways are very close at Hobby; so in the SOP; it says Local must notify Ground that an aircraft is landing Runway 12L either verbally or in the scratch pad; I wasn't verbally notified and I don't know if it was in the scratch pad. Recommendation; I recommend that I ask for more good pro-time next time I do more training. Also; immediate repeal of the new taxi rules and less closed taxiways and runways at a specific time; spread out the closings over a longer period of time so less things are closed at the same time. I also think that I should take a longer look at the aircraft on final to make sure what runway they are landing before I start a crossing.