Resource Pack Difficulties, HELP!

Only blocks that are transparent in vanilla allow for transparency, there's currently no way to enable this for other blocks. The only way around this would be to modify the block model of blocks this can be placed next to (sandstone in your image for example) to always show every face, but this will have a big impact on performance.

fixed the image embed for you

Oh, this is what happens when you don't have transparency enabled on that model, is there an option available to toggle transparency? If so, it's what you need.

I believe what you're looking for is the element cullface which you can read about a little here https://minecraft.gamepedia.com/Model#Block_models although you can find much more information about it by surfing google responses. Sorry but I haven't personally had the need to use this element before, so I can't give you a full detailed response, but I'm certain it's what you need to fix your issue. The old glowstone block was solid so it doesn't render the faces that a player shouldn't be seeing, they've been culled, but your new model means you need new cullface elements for it to display like a torch rather than a block.
I've never used a model editor before but you should be able to copy/paste the cullface arguments right into the .json file after you have it generated. Hope this gets you headed in the right direction.

Not sure if it's fault of my browser, but image doesn't appear.

Im agreeing with Wiki, because ive made texture packs before and I had that problem. You just need to make them transparent. Thats all. However, if you cant make them transparent then you need a different editor. Maybe.