I bought a small pump that was from the VAG group (VW Audi Seat Skoda etc) paid a tenner from an autojumble, it is about 17x17x7cm in it's plastic case. You could strip it out of the case and tailor the length of the cable (about 3m as std) and it would (Ithink) fit under the seat. I plan on keeping mine in a pannier. For day to day I think I would carry a puncture repair kit incorporating some gas capsules.
Probably can't get one that works from the bikes supplied socket. They tend to use more than 5 amps which will trip the protection device. So, one way around this is to have a fused connection to the battery which has the same DIN plug. You could use this for charging the battery / heated jackets etc etc as well.
I bought an 'Airman' pump, from Wilkinsons would you believe, for about £10. I cut off the cigarette-lighter plug and replaced it with a plug from Maplins that fits the two-pin Optimate tail lead already connected to the bikes battery. Easy!
Yep, get an Airman unit from Wilkinsons c£8, cut the plug off it, but fit croc clips, as it can be used on other bikes too. The battery terminals on a GS are soon exposed once the seat is removed.
Yep I've got a slime pump comes complete with extension lead, crocodile clips, accessorie plug all in a compact carry case - and it works a treat- Top piece of kit !