During the 60 day notice period, you are still an employee of Wells Fargo. The 60 day notice is the WARN act notice required under Federal Law for layoffs. On the 61st day, your employment ends and your severance begins.
They pay severance every pay period to maintain your health coverage and Wells Fargo continues paying their portion of the health insurance cost. You notify Wells Fargo when you have new employment and / or are covered under new health insurance. At which time, they pay out the remaining severance as a lump sum.
If you start working for another employer during the 60 day notice period, you can be terminated immediately for violating the HR policy against doing the same work for another employer.
Now Wells does allow a second job if it does not conflict with your Wells position work schedule and is unrelated to your position for Wells Fargo. For example, you work on weekends for a DIY store to earn extra cash during the holiday season. Since a DIY store is not a financial institution and you are working outside your normal Wells work times, you can without violating HR policy. However, you can’t work for Chase while still in the employment of Wells Fargo.
Read the HR handbook on secondary jobs or business. You agreed to it when hired and annually acknowledged.