its starting to piece together now. I read Lectric Limited information and looked at the picture and still was somewhat confused, I got tunnel vision. I went to the movies came back and read it again and it hit me like a ton a bricks. I see that it clips on with pressure of the connector on top and it can somewhat swivel and stay connected. I was thinking it was a push on type like a bullet connector duh I think I got it. I emailed the Lectric Limited to verify. I will post their replay. Thanks everyone and you Batamos for the link it had some good info.

oh when I was talking about removing the nut on the gauge I was referring to installing a ring connector and then replacing the nut it is threaded only on the temperature gauge and fuel gauge. I do not know if other years where like that or not. My buddy has a 58 3100 and when we were looking in the aftermarket catalogs his sending unit where it mounts into the engine is smaller not like the 1/2" size as in the 56.

Originally Posted by bartamos
OK so we now know that you only want info for connection to the sender NOT the gauge. Here is the complete story of senders. You seem to have the correct one for cylinder head mount. After reading the history, Click on "Repair Components" scroll down to "Temperature Sending Unit Lead Repair Kit" to see the connector you need for the pin type. I thought you had the "T" type "Hat" because most internet vendors show that style for 1956. After reading the link here, I see how confusing this 55-56 deal is and that previous owners may change things. Anyhow now you finally have the answer and the place to buy what you need.
http://www.lectriclimited.com/frequently_asked_questions.htm#F02
The 3rd white connector from the top is probably your choice for the sender pin because it can't rotate into something hot because it's round.

P.S. If those studs in your pic are on the temp gauge, they are not for a ring tongue. I do not see threads. You should not take the nut off IMO. You may need what I think I see in the lower right corner of the "Repair Components"/Temp sender unit lead repair kit" picture. I am pretty sure the "L" shaped Gray connector/contact set is for your gauge.
You can also see them in this pic.
http://www.trifive.com/garage/56%20Chevy%20Assembly%20Manual/12-4.gif

"As I lay rubber down the street, I pray for traction I can keep, but if I spin and begin to slide, please dear God protect my sweet ride." -Amen

56 Chevy 3100