I have found a few items that do a limited version of what you are looking for, and made a comment about my own experience.
Warding bond (2nd level spell)
This is a second level spell and lets the caster know when the other recipient takes damage, because they feel it too!
This is a very powerful and very risky thing to keep as a permanent effect however, and potentially restricts your ability to create separate adventures should they ever be apart (because one can end up starting a fight almost dead simply because their twin fell off a cliff at the wrong time). The spell has a 60ft range but you can ignore that for this purpose.
Ceremony: Marriage (1st level spell)
Another pretty powerful effect, for 7 days the couple get an AC bonus when in 30ft of each other. This isn't far, but seems to reflect that they are more resilient because of proximity, so that kind of effect could be replicated, and the characters would know when it ends because some bonus stops working (IE: they stop getting that safe feeling).
Sending stones (item). Or the sending spell (3rd level)
The item allows the players to send a 25 word message once per day. Given this is a 3rd level spell it can be quite powerful, but as it is limited to the 2 characters it is less powerful. You could even theoretically limit it to being triggered by certain situations, or let the players trigger it while you decide on the message.
When I did this, so it is not specifically sticking to your criteria, I tied it to 'when it would be fun' which is probably closest to my suggestion of the sending stones above. Basically when I thought I could use the ability to create an interesting narrative I invoked it, but gave the players no control over it because I didn't want them potentially gaming the system, or thinking it gave them permission to split the group.
One example was when one twin received a vision by touching an item, I let the other twin also see the same vision.
This way you have control over how powerful the bond is and how it works. One time they might get an emotion, other times a vision, and sometimes maybe even words, whatever works best for the situation.