What diameter of Metal Gate posts are needed for a 10′ x 4′ tubal gate

Assuming that they are round metal poles that are generally used for chainlink, the 'corner' poles are what you generally use for a gate. You pretty much use corner poles anytime you terminate a run of any kind, and a gate opening is a termination. The actual gauge isn't going to matter so much as the diameter of the pole, you need to make sure your gate hardware will fit the pole. Since your are going with wood, the extra few bucks for the thicker gauge is probably worth it, the actual diameter should be about the same either way.

Also, make sure you measure the opening correctly before concreting the poles in. Depending on the hardware you use you may need to leave extra space. For pre-fabricated chainlink gates, you need something like 39 inches for a 36 inch gate. Since you are using wood, I assume you are fabricating it yourself, but you'll still want to make sure you leave plenty of room.

Rule of thumb is that 1/3 of the post should be in the ground. A 6' fence should be sunk into the ground 3', so you'd need 9' posts.

As Shirlock states, even that won't likely support an 8' wide gate. Two 4' gates would definitely be a better option.

Perhaps the easiest solution, however, is to not even make a gate. Instead, build your fence and then make this an 8' panel that is attached with temporary fasteners...such as bolts. On the rare occasions that you need access, unbolt the fence panel and remove it completely--thereby negating the need for the two posts to cary the load of a cantilevered gate.

On the plus side, it's less gate hardware you need to buy and deal with.