Disclaimer: My first(closed) question about this subject was closed in May 2015 and there was none of the information below on the internet, meaning that maybe you will have to persevere and also give some time between your searches.
The main method I've used to find this game was, of course, affected by an immense luck: reading NES news and waiting for information about this unlicensed game to reach the internet. Searching for "unlicensed", "pirate" and "tank" got me nowhere in my hunt for this game. I would be happy by just finding some of the game screens and its music you know, to feel the nostalgia even if I didn't find the ROM.
I had almost given up on searching this game, but this "new wave" of unreleased Nintendo stuff we are facing today(Playstation Snes, Star Fox 2, Sim City for Nes) uncovered a Caltron 9 in 1 cartridge with unlicensed games that were never released, and it was on auction on Ebay.
As soon as I looked at the home screen and got the "Tank" at the list of games, I've searched for "Tank Caltron" on Google, that sent me to this video(as you can see, I'm the only one that commented on that footage). The only indexed game with Caltron publisher at NESGuide was the old 6 in 1 cartridge (that doesn't have Tank).
This also led me to another research based on this company alias (Youtube video description) and I could find that NTDEC was the most popular alias to this company in Brazil, hence the "NTDEC" at the opening. Searching for "NTDEC", "unlicensed" and "lists" I could find:
Things to pay attention for when searching for unlicensed games:
- Game publishers have aliases. NTDEC for example, had 4 of them.
- Sometimes, unlicensed games are called "bootlegs" but they aren't a modified version of an existing game but a mesh-up of sprites and sounds from other games.
- Search for those "X in 1" cartridges that comes with clones(Famiclones in this case). They could be holding the game you are looking for, giving additional assets.
- Also, try to search online for Famiclone bundles info if you owned one that has the cartridge you want. Mine unfortunately was a Milmar Top System(brazilian online store) bundled with F-15 Civil War on its package. None of the other bundle options of Top System had "Tank". The game I was looking for was part of another clone bundle that I couldn't remember, which a friend of mine owned but he sold me the cartridge only.
- Keep tracking for words like "Nes Cartridge Ebay/auction/bid" at the news section of search engines.
- Use online image search if you know the cartidge uses some weird case like the one on the question(instead of those pretty common yellow nes 60-pin unlicensed cartidges, or de default gray 72-pin nes cartidge for example). Maybe you can find someone selling the game or a blogpost about it where you can ask things.
- Have the physical cartridge and put it to play (be carefull with old cartridges and old videogames being turned on). It may sound obvious but the cartridge I had with that game got lost during city change at my childhood, making this quest way more difficult.
Other interesting sources I found during my hunt: