"I second that motion" or "I second that notion"

It's motion. It's more like the use of motion in law. It's a noun (i.e. you file a motion or move to do something). So if someone where to make a motion (make a suggestion), you would second it if you agree.

It's completely idiomatic, but that's the use of motion here; it's not a legal term.

Me: I move that we go out for dinner.
You: I second that motion!

The correct phrase is "second that motion". It originates from parliamentary procedure and is commonly used in meetings of all kinds of clubs and organizations.

Wikipedia defines second thus:

In deliberative bodies a second to a proposed motion is an indication that there is at least one person besides the mover that is interested in seeing the motion come before the meeting.

and motion thus:

In parliamentary procedure, a motion is a formal proposal by a member of a deliberative assembly that the assembly take certain action.

Where "second that notion" is used, my guess is it's done knowingly as a pun or unknowingly as an error.