The manual should solve the issue that the respondents have to click the "next" button instead of automatically getting to the next page.
If I get you right, the problem is: You want to show the button on one page, and hide it on the other one - and both around the same time.
I would recommend that you store a PHP or dataset variable for each day. I'll use an internal variable here (not a PHP variable), because it seems useful to me in your contect to see the times in the dataset. What you would to, is to set the current timestamp to an internal variable on the first page of a day, such as:
if (!value('IV01_01', 'code:ifany')) {
put('IV01_01', time());
}
On the page with the next button for page 1, you can check if 23 hours have passed.
$started = value('IV01_01');
if ($started < time() + 82800) {
goToPage('next');
} else {
text('XY00'); // Say goodbye for the moment
buttonHide();
pageStop();
}
Create internal variables for each day, and replace the IV01_01 in the code for each day (IV01_02, IV01_03, ...).