Parking Brake:
Sticking micro switch. Remove right side panels and find the front pulley for the parking brake cable. Operate the parking brake and observe how the tab operates the micro switch. The switch is actuated when the brake is disengaged, and released when the brake is engaged. Switch plunger and operating arm need to operate freely without any drag. Check if arm is bent and straighten if necessary. Clean up the area - compressed air - a spritz of lube such as spray silicon or CRC.
Shifting:
A little more complicated.
The basics - the engine has to be running.
Even though I don't have to on the 2012 RT, some folks say that they must have their foot on the brake in order to shift out of Neutral. If it only affects shifting into Reverse, then focus on the R button - any binding or dirt.
Inspect the shifter arm under the left side for signs of looseness or excessive wear or play between the arm and the shaft. Lots of history on SLs site on that. Do a search if you find that problem.
If maintenance history isn't well known, consider either replacing the HCM oil filter with new, or doing a complete oil change and replacement of both filters.
Yes, maintain proper oil level. And there have been instances of failure of the paddle shifter switch. As a last resort, you may have to remove the HCM suction line from the oil tank and clean the screen. That is hardly ever required. It's usually something simpler.
Any questions about how the SE5 transmission works, refer to this document:
https://drive.google.com/file/d/13kC6u-tRszWUVQvht8jhUZgENl_qlTRo/view?usp=sharing
P.S. - And as a general rule, whenever anything doesn't operate correctly on a Spyder, even if it doesn't always make sense, ensure you have a good battery, and battery connections that are clean and tight. If you still have the 2012 battery in it, dump that sucker and replace it.