I PCS from Korea in less than 2 months and I still have no sponsor. What should I do (I emailed Fort Hood sponsorship office no response)?

The sponsorship program has been broken since about 1984, it has been hit or miss, posts to post, unit to unit with no real constancy...
The FH Sponsorship office is in the Copeland Soldier Service Center, and that has a front desk manned 24/7 [login to see] call and ask to speak to the senior person,,normally a SSG, but I have seen SFC, MSG on the desk as well. (and PFC, SPC)
Ask them to double check the Sponsorship office contact info for you, and ask if they could walk over to it, get a name and a good contact number plus time that persona will be available to take a call.
When I left FH 2014 the office had small group of folks, Mil and Civ, say 8 or so...assuming the program is still active, there should be someone in the office 5 days a week during business hours.

If none of that works, message me and I'll go on post and be a squeaky wheel

You'll likely be going through central in processing and the unit you get assigned to as replacement will acquire you so they may not even know for sure you're coming to them yet. Are there any specific questions you might want some answers for in advance of your PCS? Do your orders have you slated for a particular Brigade or Regiment and from there you might get a sponsor to contact but unlike going OCONUS, sponsorship is a little broken as one of the other responders has said.

You probably won't have a sponsor until you reach your battalion. Korea won't recognize your sponsorship request until you are listed as in theater. Good luck!