I did answer: A chassis is a chassis. A tube is a tube. They all connect the same way. (and an arcade tube is the same as a TV tube---the things you read on 8liners applies to arcade tubes as well) Read the FAQ's about connecting replacement chassis or TV's and you will know how to connect any arcade chassis.
Specificially:
Generally all 13" tubes have an 8 pin connector with a small neck. (Whereas 19" tubes can have 8, 9, 10, 11 pin connectors and small or large necks). You're probably safe connecting it, but I'd do a lookup on the tube part number online and see what the pinouts are and compare them with the labels on the neckboard you're connecting to so you don't fry something if they don't line up.
Yokes vary in types of connectors significantly. They might just fit on the main chassis board, or they might require modification to plug in. They also may use the standard Red/Green/Yellow/Blue or they may use other color wires and you have to measure their DC resistance to determine which are which.
Yokes may also vary in the amount of impedence they have -- high or low, at least for 19". I don't work with 13" too much so I don't know if they're the same, Ken can probably answer that. You need to measure the vertical winding DC resistance and see if it is 15 ohms or less -or- 50 ohms or higher, and check if your chassis supports it.
The yoke has absolutely nothing to do with the tube/pin count. The yoke is the plastic piece that has copper wires wrapped on the outside and inside of it and slides on over the neck of the tube. The yoke deflects/steers the electron beams (like a Yoke on an airplane--it steers the airpane left/right and up/down). The Tube itself has the electron guns, focus and screen grids and you connect those at the neck of the tube with the neckboard. Without a yoke, the tube would send the electron beams to the center ofthe screen in a single dot and quickly burn a hole in the phosphor. THe yoke makes the beam move left to right and up and down..
Also, you can't just attach the neckboard and red anode wire and expect it to work. You also need to connect the ground wire that touches the outside of the tube's aquadag and connect to the ground pin on the neckboard.