Rising and falling intonation
Solution 1:
All spoken languages use intonation, either for meaning of sentences, meaning of words, or as a byproduct of pronunciation. That said, each speaker will have their own way of intoning words and phrases that fits their personality or mood-at-the-moment. Generally speaking, though, your first sentence, in English, is an "either or" tone structure. Usually, the first choice is spoken with rising intonation and the second with descending:
Would you like X (up) or Y (down)?
What is confusing for foreign speakers is that they are told that in English, sentences are designated as question sentences with a rising intonation at the end. This is only partly true and depends on the accent of the speaker. For example, in the question,
"Where is the bus stop?"
The rising intonation happens on the interrogative, "where," and not on "stop." However, I have heard people with an Irish accent speak the sentence with a rising tone on "where" and "stop," which for me seems unnatural. I teach American English with a "Chicago Broadcast" accent.
In examples 2 and 3, the names "Tim" and "Jack" are being emphasized. I don't know the situation, so I can't really say why those would be stressed, but they seem unnatural to me. One thing I have noticed is that when trying to see if something "sounds right," the repetition tends to make anything "sound right." Example 2 seems like a speaker trying to impose question intonation on a sentence which should have "either or" intonation.
If you'd like to explore this subject more there are a few books. I have used this book for several years, and found it very helpful. Also, I have followed this Youtuber for a while and she has good information. Keep in mind that English is spoken in many different ways, so a British speaker (and there are hundreds of accents) has different intonations that an American or Australian or someone from India.
Solution 2:
Do you want me to call Tim' or Jack?
Do you want me to call Tim or Jack'?
Do you want me to call Tim' or Jack'?
It is almost impossible to represent intonation without using musical notation and even then there are microtones that cannot be shown accurately.
Without intonation, the question, "Do you want me to call Tim or Jack'?" is ambiguous.
It can mean
(a) Do you want me to call Tim or alternatively do you want me to call Jack?
(b) Do you want me to call Tim or Jack or neither?
Here is my diagram showing a possible very simplified intonation (I am a musician).
Note that (a) starts low, rises for "Tim or" and drops again for "Jack".
(b) starts high and drops for Jack.
If I have time I might write this out in musical notation but it won't help if you don't read music!
However
As a musician I can tell you that these are not unique patterns and that there are subtleties in microtones all the way through. The only way that you can truly get this right is by listening to native speakers.
Solution 3:
The whole issue of high and low intonation is complex and involves style of speech as well as meaning.
Take for example, those who upspeak. To me it's an annoying style of speaking which is becoming more and more used as far as I have noticed. This is for sentences as well as questions.
With questions, it is appropriate sometimes to raise intonation at the end of a question, but not always. Listening to my intonation, if there is only one option at the end of the sentence, for example,
Do you want me to call Jack?
Some of the time...
The intonation is raised at the beginning of the name Jack and lowered through the name to the end where the intonation is the same as midrange of the rest of the question (main intonation) with an almost unnoticeable dip towards the end.
If there is more than one option, with all but the last option, the intonation stays at the main intonation and the last option starts at the main intonation and finishes lower.
With your examples:
Do you want me to call Tim' or Jack?
Do you want me to call Tim or Jack'?
Do you want me to call Tim' or Jack'?
If the apostrophes indicate high intonation, number 2 would sound unnatural to me, whereas number 1 is a question with a definitive ending and number 3 has no definitive ending, allowing the answerer to respond with an alternative name to Tim or Jack.
But, there are other times where the intonation is different.
With one option, the beginning of the option will be higher than the main intonation and dip to the main and quickly raise again slightly higher; and with more than one option the previous options to the last will be at the main intimation throughout followed by the last option which has a dipped intonation (high at start dipped to low and quickly raised to slightly high).