Is it a general practice that one would switch to non-dominant eye, when shooting weak-side?

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I don't think so.
Personally, I am RH-Right eye but when I shoot lefty, I cant the pistola towards my right eye.

Right now, I'm shooting close range with 2 eyes open. Out to 20-25 yards takes some concentration. Seems to work for me.

Is it a general practice that one would switch to non-dominant eye, when shooting weak-side?

There are no hard and fast rules here, but the general guideline is to treat it just like a cross dominance situation.  Continue to use the dominant eye and learn to bring the weapon into the line of sight of the dominant eye and avoid bringing the head to the weapon. 

For myself, I am the exception, in that I am ambi-ocular in that I do not have a dominant eye.  Both eyes share similar dominance traits and from one part of the day to the next I can have dominance switch between eyes.  This also wreaks havoc on trying to shoot two eyes wide open on a dual plane sight (irons), red dots are not an issue.  Because of this situation and not necessarily knowing which eye is going to be dominant at that moment so I automatically squint to force dominance to whichever side I chose.  I will use the same eye as the side that I am shooting from and squint the opposite eye. 

I never have cared for the term "weak side."  It's not that I've got some politically correct rub against it, I think the term is accurate enough.  It's just I don't see anything weak about being on the wrong end of a gun, regardless of which hand someone is holding it with.  If there's a loaded gun in your hand, that's your strong side!

here's a video that was linked on hkpro today that is appropriate to this discussion
in this video, it's "other strong hand"

After a few courses, I've come to refer to them as strong side and support side.  Avoid calling shooting from my left side as weak since you shouldn't have a weak side.  Yeah, it's largely mindset, but yes, if you train and shoot regularly from both sides, then in theory there would not be a weak side.  When I was shooting often, I was fairly comfortable shooting with both hands, but moreso with the carbine.  Where I really can tell a difference is in the reloads or malfunction clearance.  You also have to be careful/mindful if you're using a sling on when you transfer sides, how you do it and where your sling ends up.  I've since switched up how my sling is secured to the gun after getting caught up in a couple courses of fire in a carbine class. 

For handgun, I'll slide the gun over to shoot with my dominant right eye.  For carbine with red dot, I'll usually wink (or squint slightly) my right eye just before putting my cheek on the gun and once my left eye picks up the dot, I'm good to go.  It's like once the left eye picks up the dot, it sort of locks onto it. 

always a struggle here and I hate my friggin' lopsided contact prescriptions can't get it right still.  naturally right eye dominant but have cross eye dominant at times.  so I squint to force either side but would like to play with support side + right eye and not squinting to force the left as usual.  long gun the eye matches the firing hand but am not ambi by any stretch.  would do better just throwing gernades. 

Lots of shooting classes go into one arm shooting but manipulation with a firearm one handed should also be discussed/taught in a controlled environment. Out of a few classes I have been too in Washington and Cali only one discussed and went through the course of fire with one handed operation.

The dot torture drill is good practice. HDF normally does it during their pistol courses.

•Dot 1 – Draw and fire one string of 5 rounds for best group. One hole if possible, total 5 rounds.
•Dot 2 – Draw and fire 1 shot, holster and repeat X4, total 5 rounds.
•Dots 3 & 4 – Draw and fire 1 shot on #3, then 1 shot on #4, holster and repeat X3, total 8 rounds.
•Dot 5 – Draw and fire string of 5 rounds, strong hand only, total 5 rounds.
•Dots 6 & 7 – Draw and fire 2 shots on #6, then 2 on #7, holster, repeat X4, total 16 rounds.
•Dot 8 – From ready or retention, fire five shots, weak hand only, total 5 rounds.
•Dots 9 & 10 – Draw and fire 1 shot on #9, speed reload, fire 1 shot on #10, holster and repeat X3, total 6 rounds.

Ive heard about this but never tried it, gonna try it tomorrow morning and see how I do.