Extension cord recs when there’s no info on outlet

Yes, as short as you can, so long as it is long enough to be safe!

 

I think a lot of people have made this overly complicated - You need an outdoor extension cable rated for 15A. Use only one extension cable (so buy a single extension cable you can be sure will reach, don't daisy-chain extension cables). Lower AWG wire is obviously preferable, but of more concern is protecting the contacts in all of the plugs/sockets. You'll want a way to keep all of the contacts free from rain/elements. See this if you haven't - corrosion buildup can increase the resistance of the contact, causing it to draw power, and heat and melt the plug:

Melted extension cord socket | PriusChat

As far as the wall socket you'll find, most likely the socket is the super standard 120V, 15A plug, connected to a circuit with a 20A breaker. These are standardized by the national electric code. If the left connector on the socket has a horizontal line in addition, then it's a 120V, 20A plug, most likely connected to a 25 or 30A breaker (though it's not rare for these too to only be wired to 20A breakers). These are completely safe to plug into with the normal 3 prong plug.

 

How long a cord do you need? Exactly.
As you're not charging with an L2 charger 240v, but an L1 120v, a 10-3 is plenty, but not 50', possibly 25', easily 10', 12-3 isn't really a good idea.

 

25' 12/3 is plenty. if you're nervous, go 10/3, but notice the unnecessary weight, flexibility and cost difference.

 

In the pictures I see the other plug is being used by something. It's a good idea to find out what is plugged into the other outlet.
You'll be ahead of the game if something unforeseen happens while you are charging.
I can't tell from the pictures how high the outlet is, but you may want to make sure you can reach it if it is as high as it looks,

 

I have old eyes, but i THINK it is a Rain Bird sprinkler timer, in which case if he blows a breaker, the grass turns brown.

input 120 VAC/ 0.3 AMP/ 60Hz so it is not drawing much of the 15 amps he is sharing with it.

If anyone can read the logo, please tell us.

Google images almost always shows them with the cover open, as that is the interesting view.

 

Close. It's a Rain Dial sprinkler controller, not Rain Bird.

 

This manual hints that this may draw 30 watts or 0.4 amps out of the 15 amp breaker.
http://sprinklertalk.com/product_manuals/manuals/Irritrol/Controllers/Rain%20Dial%20-R/raindial-userguide.pdf page 12