Just a thought, if 2A is for "Radio Memory" on some models it might have constant power and not be controlled by the key switch. Just something else to consider when looking for a power source, do you want "always on" or "switched" (controlled by key switch)?
For the electrical manual genius...how do I hook up to 2A...from the FLHR section in the manual. For other models this feeds radio memory...see picture 2 for reference.
FLHR
You just need a couple parts.
Look at the link from installing heated grips. Figure 6, you need something similar, your parts guy may be able to order some. Like Charlie said the picture you posted ECM, Battery and Radio Memory are hot 24 - 7.