The AdvancedPublisher stacks might be the way to go, for the time controlled aspect. Try the free demo version. The expiry stack is less suitable for recurring dates / time.
I envisage you could add the AP Base stack to the page first.
Add an AP Days stack, to control what days of the week the content should be shown.
Within AP Days, drag and drop an AP Time stack, to regulate what what time the content needs to be shown:
In the above example, the text ‘we are live’ would only get shown on a Tuesday morning, between 9am and 10am. Obviously you can replace the text with another stack type, like a button.
I don’t know of any button stacks that have a pulsing effect. But I have put together some HTML and CSS code for one here:
The HTML code goes anywhere in your page where you want the button to show. The CSS goes in the custom CSS box, in the RapidWeaver Page Inspector. Customise the link address and label as required.