Reydel,
The British view (as taught at Dratmouth at least) has always been that we actually gave you all the signals that we didn't care. The three clues were (supposedly):
1. British Nationality Act (1981) differentiated between British citizens and British Overseas Territory Citizens.
2. We were going to scrap HMS Endurance.
3. We were selling HMS Invincible to the Australians.
The deduction was 'they don't really want the Falklands - they consider the inhabitants to be less British, they don't care about the South Atlantic, they're no longer interested in fighting overseas'.
There are compelling reasons for thinking that you were right on all three counts. But, the military occupation of the islands was enough to create a completely new political landscape.
Even then it has been recounted that Mrs Thatcher was advised by some that we couldn't or shouldn't do anything. I think First Sea Lord gets the lion's share of the praise for saying that we could and should mount a military operation and Mrs Thatcher leapt at the chance.