If you can convince your Healthcare CEO that Twitter is a gateway technology from Healthcare 2.0 (Social Media) to Healthcare 3.0 (AI, Blockchain, Semantic Web, etc), and they decide to try it, then how frequently do they need to tweet?
I suggest using what I call The Bill Gates Rule.
In the first 71 days of 2018, Bill Gates tweeted/retweeted 58 times.
Thats .816 times per day, or roughly 6 tweets/retweets per week.
If your CEO is busier than Bill Gates, or has a bigger mission, then he should tweet a little less.