You have your definitions of Discretionary and System mixed up.
There are two types of Discretionary traders and both do not use any automation:
1) Gut feel or instinct as you stated
2) Rule base...type of rules that can't be automated
IMHO trading by 'rules that can't be automated' is the same as trading on gut feel.
Either a rule can be quantified and thus automated, then it will be something like 'buy if the market moves up more than x ticks within y minutes' - a very simple momentum entry - or they can not, then the rule will be something like: 'buy if the market shows strong upside momentum'.
But what is 'strong'? Well, if not defined by some objective criteria, this completely depends on subjective assessment, which in the end is hardly more than gut feel.
That being said, it's possible to mix up systematic, rule based and discretionary trading in some way. For example, one could use some quantifiable criteria to select which stock(s) on a given day to trade, the direction and that the trade will be closed at the end of day, but the decision when to enter the trade exactly is discretionary.
Whats important here ist that the systematic part and the discretionary part can be isolated and evaluated individually. In our example, the performance of the systematic part would evaluated by assuming an immediate entry without discretion. The performance of the discretionary part then is the difference between this hypothetical performance and the actual performance.
IMHO a trader unable to evaluate his trading strategies is destined to fail.