How do I explain my short employment and long gaps due to mental health?

Exodi

LostDuck said:

99% of jobs that I apply for don't respond to me, and the incredibly rare 1% that I get to speak to don't want to know anything about me other than the gaps and short-term employment. And "personal reasons", "health reasons" and "temporary employment" don't seem to cut it. 

I think this is the crux of the issue. Put yourself in the employers shoes, one of the first things an employer will notice is the gaps in your employment history, and if this isn't addressed in your CV then inevitably it will either cause your application to be binned, or at best you'll be questioned about it at the interview stage. The employer will want to make sure that you're not going to join and then shortly leave after they invest resources in training you. Dismissive responses like "Personal reasons" do not allay these concerns.

Personally, I'd properly address this point in the bud on your CV.

LostDuck said:

I think that's exactly the problem, that I don't get a chance for anyone to get to know me or how much I want the job and strongly believe I can do it and stay there, because I look too unreliable on paper.

"if you don’t give a proper reason, then you come across as not being reliable"

But what is a "proper reason"? Because I can't say mental health based on the unreliable thing, and 'personal reasons/health reasons' has always proven to not be a good enough answer and looks the same.

As you say, the concern is that you appear to be unreliable, and from what you've said so far, there's nothing to suggest that anything would be any different or that you would stick at your next job. If you don't believe yourself that you will stick at your next job, what hope to you have of convincing a prospective employer you will.

Really you need to identify (to them and yourself) the issue in the past and the steps you've taken to prevent it happening in the future.

LostDuck said:

I used to work in digital marketing, on the creative side like social media and basic graphic design but very low level, like assistant level. 

This is perfect! Personally if it was me, I'd be tempted to include some examples of your previous work in your CV - much better than a page of text, especially for a creative role like marketing/social media.