I job shared very successfully for 3 years. We were lucky to both work 3 days (Mon-Wen, Wen-Fri) so we always had a face to face hand over mtg on Wed morning. We were team leaders, and we had an additional responsibility to the FT team leaders to justify the extra day.
Some things to think about
1- shared mail boxes
2- do you want to allocate certain tasks to each person , or are you both going to do everything on your days? Or a mix of both?
3- Don't book leave at the same time, you'll be expected to be each other's holiday cover.
4- we kept a running log for each other, of what had happened during our par of the week;issues, resolutions, outstanding tasks etc during our half of the week. We actually did this in an A4 desk diary, but I'm sure there are more techno ways to do it now. .
5- we had to encourage other staff to see us "as one". So, no "I need to speak to Jane about this", but "I need to speak to Jane or Lucy about this".
6- part of our role was appraisals, and we discussed these together beforehand to get a full picture of that staff member. With a couple of particularly trick members of staff, we both did their appraisal.
7 have a very clear line of sight of what your managers are expecting from you. You both need to perform well at the standard expected.