What I would do is:
- Have an Updatecontact activity at the end of journey one to insert a value into a DE that you then use as a flag for beginning Journey 2.
- Create a SQL Query in Automation Studio to run every day or so to find those that have this flag and the date of exit was 1-2 days ago then push them to an entry DE for Journey
There are other ways, including via a custom built Journey Log, API tracking events, etc. But I find the above to be the easiest to implement and execute.
Sample SQL:
SELECT SubscriberKey
FROM [myDE]
WHERE exitFlag = 1
AND CAST(exitDate as Date) = CAST(GetDate() - 2 as Date)