The tire pressure sensor is built into the valve stem on my 2006. Pretty sure yours is the same. It could be that your spare doesn't have the sensor built into it, but more likely the battery is dead. The batteries can't be replaced. You have to periodically replace the sensors. They run around $65 each, but if you look around, you can get them for about $25 each online. I bought one this past summer and have another one that needs replaced right now.
Check Partsgeek.com. I found mine for $24.60 there.
1998 TJ Sport, 4.0L - 5 spd -Suffering from frame rot
2006 Grand Cherokee Overland (5.7L HEMI)
HEMI Club Member #53
2003 M-B C240 4matic