Everything you said is essentially correct. So, I’m not sure what you’re uncertain about.
I would say it in the following way:
You can think of a currency pair, not as the relationship between two currencies, but simply as a single “thing”.
[B]If that “thing” is going up in price, then you want to buy it; if it’s going down in price, then you want to short it.[/B]
There are two sides to that “thing” (that pair): the base-currency and the cross-currency (personally, I’ve never heard the term “quote currency”). If the price of the pair is changing, then one or both of the currencies in that pair is changing in value.
If, for instance, the pair is going up in price, then one of three situations must be occurring: (1) the base currency is increasing in value, (2) the cross-currency is decreasing in value, or (3) both are happening.
Looking just at this currency pair, you can’t determine which of those three conditions applies.
In order to determine which currency in a pair is responsible for a particular price movement, either (1) you have to determine the fundamental cause of the price move (good GDP numbers were released, a terrorist attack occurred, etc.), or (2) you have to determine how the overall market valuations of the individual currencies in the pair are changing.
The idea of a fundamental cause is easy to grasp. And it’s pretty easy to identify fundamental causes for price movements, after the fact. It’s much trickier to determine, ahead of a price move, how a particular fundamental development will move prices.
Overall market valuation is determined by purely technical analysis, without regard to what fundamental cause moved prices. Overall market valuation simply refers to how the base currency in a pair is moving versus all of its major crosses, and how the cross-currency in the pair is moving versus all of its major crosses.
So, for example, to analyze an up-move in the USD/JPY using this (technical) method, you would look for similar USD strength in the other USD pairs, and/or similar JPY weakness in the other JPY pairs. You might find one condition, or the other, or both.
Finding both conditions would tell you that a long USD/JPY trade is probably the best trading opportunity of all the pairs you have just looked at.
Clint