I have always, as you say, "split them by the count of notes." It's a multi-step process of:
- Ignore the triplet aspect of the rhythm and focus only on the note values themselves.
- The total duration of these note values will be equal to three of some other note value.
- This other note value is the basis of your triplet. The triplet will last the duration of two of these basis note values.
Let's take your first unequal example of an eighth, two sixteenths, and an eighth. Our first step is to ignore the triplet aspect of this rhythm and focus on the eighth, two sixteenths, and the eighth. The total duration of these notes will be equal to three of some note value. The eighth, two sixteenths, and eighth are equivalent to 1.5 quarter notes, or three eighth notes. The eighth note is thus the main indicator for this triplet.
A triplet consists of three note values that take place in the span of two. So this first triplet, because it's written in the duration of three eighth notes, will actually last the duration of only two eighth notes (i.e., a quarter note).
From there, it's just a question of subdividing. Practice your "regular" eighth-note triplet, then try subdividing each of the eighth notes into sixteenths. Finally, remove the extraneous sixteenths and perform the eighth, two sixteenths, eighth triplet as written.
I know how cumbersome this answer is, so let's try your second example, too. The triplet has a half followed by a quarter. Let's ignore the triplet aspect and only focus on those values: a half and a quarter. Then, we know that the total value of that half and quarter is equal to three of some single note value. The half and quarter are three quarter notes in length, so the quarter note is our main rhythmic basis.
A triplet is three note values in the place of two, so this quarter-note triplet will last the duration of two quarter notes (i.e., a half note). I recommend practicing this triplet as if it were three articulated quarter notes, and then slowly removing the articulation on the second quarter note.
One more example may be helpful: a triplet of a quarter, dotted quarter, and eighth. Determine the answer yourself, then click the spoiler text to reveal the answer.
The quarter, dotted quarter, and eighth are equivalent to three quarter notes. This triplet will thus last the span of two quarter notes, or a half note.