Dye testing finds cracks. You don't have a crack, but a brand new gouge, so dye testing would not tell you anything new. I have a degree in engineering materials. The following are just my impressions, based on what I see in the photo.
A gouge is bad on the outside of the wheel only because it provides a stress riser that can turn into a fatigue crack with use, and eventually fail. That said, it will likely take a long time for your gouge to develope into a crack, and even longer to fail. If you only use the car for normal driving, I think you will not have a problem. If you intend to run the car hard...then I would be much more concerned about it. RPM is the factor. Double the RPM and you quadruple the loads on the wheel.
Failure of an auto flywheel is a bad thing, as it is located in a place that will amputate feet...also a bad thing. I would place your gouge in the catagory of a very low chance of failure...but having a very high chance of intolerable consequences if it does fail! Here is the order of best to "least best" fixes.
1) The best fix is to have a machine shop turn the outside down to remove the gouge. The 1/2 pound or less of weight loss will not be noticeable, and the wheel will actually be stronger since the diameter will be slightly reduced. This, of course, is also pricy. About $100 per hour at a machine shop...and I think an hour would do it. Some shops will "gouge" you with set-up fees, though.
2) If you plan to drive the car around town with only occasional high revs, you can "dress" the gouge and forget about it. That's what we do on the compressor blades on jet engines. You cannot trash a multi million dollar motor just for a little nick on a blade, like yours...and nicks occur very frequently in the life of an engine. Replacing a compressor blade requires complete disassembly of the engine - also very expensive. Dressing is accomplished by smoothing the gouge with an abrasive disc. There must be no sharp edges...the gouge is changed to have only very smooth surfaces, inside and out. Finish with fine abrasive so the area is shiny smooth. Cracks ALWAYS begin at a stress riser. The idea here is to smooth your stress riser so it goes away. It's low tech, but it works!
These TR's are not really high reving, compared to newer cars. I personally would dress it and go have fun. If it still concerned me, I would open the bell-housing cover at the next couple oil changes, just to make sure a crack hasn't started. (that's when dye penetrant would be useful)
Remember, if you take a lot of metal off in dressing...you may have to re-balance the wheel so your shifter knob won't rattle!
Again, these are just my thoughts. Ultimately, it's your friend's toes, so it is his decision.
John