I tried to find out more detail about the security measures, and I couldn't find anything that helpful, but this quote from Wikipedia sheds some light on this:

Cardinals who arrive after the conclave has begun are admitted nevertheless. A sick cardinal or a cardinal who has to use the lavatory may leave the conclave and later be readmitted; a cardinal who leaves for any reason other than illness may not return to the conclave.

...

Priests are available to hear confessions in different languages; two doctors are also admitted. Finally, a strictly limited number of servant staff are permitted for housekeeping and the preparing and serving of meals.

Secrecy is maintained during the conclave; the cardinals as well as the conclavists and staff are forbidden to disclose any information relating to the election. Cardinal electors may not correspond or converse with anyone outside the conclave, by post, radio, telephone, internet, social media or otherwise, and eavesdropping is an offense punishable by automatic excommunication (latae sententiae). Only three cardinal electors are permitted to communicate with the outside world under grave circuмstances, prior to approval of the college, to fulfill their duties: the Major Penitentiary, the cardinal vicar for the Diocese of Rome, and the vicar general for the Vatican City State.^[3]

This sounds pretty elaborate and careful to me. So the only way Tisserant could have gotten out would have been if he had pretended to be sick; but he would have had to convince the two doctors that he was sick -- and not only sick, but so sick that they were not capable of treating him there in the conclave.

Unfortunately it doesn't give much detail as to how these regulations are enforced, but it makes sense to assume they are actually enforced and are not simply requests, i.e., that the cardinals are not just asked to observe these rules, but are physically prevented from breaking them.

I'm not saying this disproves the story about a cardinal leaving the 1958 conclave, but it certainly makes me wonder how such a thing could have happened, and why the people who claim this happened don't attempt to explain how it was possible, when according to the rules of the conclave it doesn't appear to be possible.

Okay, fair enough, so it's not the Swiss Guard who guard the conclave. But that wasn't my point. My point was that there are people who guard the conclave and prevent people from going in or out, for the very reason we are told about what happened in 1958 (and that was before the rules of JP2 that you mention).

Sure, but it's just a couple of people, who could easily have been cooperators with Tisserant or somehow easily influenced / persuaded by him.  There were undoubtedly a great many conspirators in the conclave.  I'm honestly not sure how they got so many Cardinals to vote for a guy like Roncalli.  It could have been an orchestrated ruse.  Push Siri out, then claim you're going for a "compromise" candidate, so you grab Tedeschini (knowing he's too old and sick to function), and then roll out Roncalli as if he were a backup "compromise" candidate, an old guy who'd have a short reign (at least that's how you'd spin him).

That type of strategy might have in fact been what Tisserant conferred about.  "We pushed out Siri but we don't have enough votes for Roncalli."  Jew:  "Pretend then that you're going for an old compromise candidate, start with Tedeschini, who won't accept due to age, and then roll out Roncalli presenting him as a backup compromise candidate."

The Swiss Guard are dudes who drink death like water

Which Swiss guard are you talking about???