I wouldn't share my Gmail password. Besides, I have two-factor enabled on my account, so the password alone wouldn't be that useful.
If you are using Gmail, you can share access to your inbox with another account. This would still let your cofounder access your inbox and read your mail, assuming that's what you are solving for. Your cofounder would also be able to send mail as you, but it will show up as "sent by cofounder@company.com".