Not knowing much about corporate law (now or in the world of Shadowrun) I've tried to come up with a reasonable explanation for why Gideon is hiding. Since this is Shadowrun it involves flying cowboy pirates. The link below describes what has happened over the last three years and what's going on right now:
VE History and Current StatusI sort of took the liberty of making my company successful but it's engineered so it would not be easy to get access to any company assets so I think it should be OK. If anyone thinks something should be changed, let me know.
Possible Character Connections:
For Trigger:
1) Trigger could have been hired to deal with the para-critter threat that VE had about a year and a half ago. This would involve going to Brukina Faso and figuring out what was eating the cattle and how to stop it.
2) Gideon has been involved in researching people and spirits somewhat associated with the Wild Hunt. It's possible that Trigger could have learned of this if she came to Burkina as in 1 above or it's possible that they could have crossed paths while trying to find info on the Wild Hunt.
3) Gideon has been close to a number of Trolls that have had big reps (Eric, A-Bomb, etc.) Unfortunately none of those players are in the game but there could still be a connection.
For Hotei:
1) Medical Clinic connection. Gideon knows several doctors: There's doc Carlos who was last seen taking care of Red, the brain in a jar. There's Dr Shaila Keigwin, the Indian doctor who ran the VE Medical Clinic, it's possible that Gideon could have relocated her and her staff to Seattle a few months back when things started getting dangerous with the Mega Corps. There's also various un-named doctors from the Gama teams that might have set up a clinic in Seattle.
2) Chance encounters. Gideon gets around and lately he has been traveling to do land speculation. Its possible the Gideon and Hotei could have met before Hotei came to Seattle.