Hey Denley. First, a little bit about codes, while the Spyder sometimes uses the standard OBD-II codes, it also uses vehicle / manufacturers specific codes. You can tell the difference - if the first digit is a number 1, that is a vehicle / manufacturer specific code. You won't find the answer in Google unless it comes out of this forum. If the first digit is a number 0, that is a standardized code. Bottom line, you don't have a problem with coolant level. There's no sensor for that.
What you DO have is a problem with the throttle body shaft or linkage, and/or the Throttle Position Sensor (TPS).
P1616 has to do with the mechanical idle stop of the throttle plates not being where the computer thinks it should be, based on the signal coming from the TPS. That can be a TPS issue, or also mechanical binding or wear of the butterfly valve shaft.
P1620 has to do with an adaptation failure of the TPS itself, where either the TPS or throttle body was replaced, and the adaptation wasn't performed. (if that was the case though, it could have appeared before now) That requires an attempt at running the Reset (adaptation) with BUDS software. Also can be a sign of pending failure of the TPS.
So first, you can keep riding and see if this was just a spurious event that can correct itself with more use. Don’t be gentle with it. I wouldn't go on a cross country trip just yet, though. Give it a couple of operating cycles to see if the light clears on its own. If it doesn't, you could go to a dealer and have them do the TPS Reset with BUDS to see if that's all you need for a permanent fix. It won't be free, but it's quick once they can get you in.
If that's not successful, or without BUDS software to attempt the Reset, about the best you can do on your own is try to find the smoking gun. Unplug the TPS connector and spray it out with electrical contact cleaner. Let dry and re-connect. You should also do a throttle body cleaning - you just need to clean the shaft where it passes through the bushings so that it turns easily. The 998 engine can blow some oil up into the airbox and gum things up royally. You don't know how it was treated in its previous life. Use some compressed air to blow out the linkage in between the throttle body and the actuator motor. Check if anything is interfering with the linkage or mechanical stop, such as dirt or critter nest. Make sure that area is nice and clean and look around for any wire damage. It's a 9 year old machine with low mileage. There's a chance that this is all you'll need. It seems to be running fine, otherwise.
The TPS is located on the rear of the throttle body assembly, the actuator and associated linkage on the front. You'll be removing some intake box and ductwork to get to it all. If you are satisfied that it's not a mechanical issue with the throttle body, then the TPS will need replaced. Replacing the TPS will require the TPS Reset procedure to be performed with the BUDS software. Either a dealer or private individual with the software near you could do that. Good Luck.