Deficiency

• Insomnia
• Migraines
• Anxiety
• High blood sugar
• High blood pressure
• High cortisol levels
• Palpitations
• Tense muscles
• Cramps
• Eye twitches

My experience

A year or two ago, my magnesium levels went pretty low (for certain reasons that I now understand), and I had pretty much all of those.
I couldn't sleep. My yearly blood tests showed that my HbA1c had gone into the pre-diabetic range (which had never happened before). I was also anxious, worrying about all sorts of stupid things that weren't really issues. Catastrophising.

I eventually realised it might be magnesium, and bought some supplements to try.
When I took one in the evening, it knocked me out flat in about 30 minutes, and I had a lovely night's sleep. Eventually my levels recovered, and now things are back to normal. My blood sugar is now back to normal, and hasn't gone up again.

Unfortunately, it's not something that can be checked with a simple blood test. Blood tests mainly come back as "OK", because the body (sensibly) prioritises it for the things that keep you alive (heart pumping), and doesn't care so much about the other things because that's the evolutionarily more sensible path.
If one or more of those in the list above ring a bell with you, well, it might be low magnesium.

Stress - the vicious cycle

To make it even worse, stress (high cortisol) actually lowers your magnesium levels, and this in turn makes it harder to deal with the stress. It's a vicious cycle - the stress is dumping the very substance that you need to cope with it. You end up in a downwards spiral that is very hard to break.

Diet

Yes, you can in theory get enough through just diet. You need roughly 300-400mg a day (depending on your age and who you ask). But if you look at what foods contain it, do you really think you're getting sufficient? Every day? I certainly don't. And that's if you have good digestion and absorption, which many people don't.

If you think you might suffer from any of the list above, you could do worse than buy some tablets and give them a go for a month. From what I can tell, unless you're suffering from kidney disease, there's no reason to worry. The NHS says "Having 400mg or less a day of magnesium from supplements is unlikely to cause any harm."

Supplements

If you do try a supplement, you'll find that there are a number of different compounds of magnesium - chloride, oxide, gluconate, malate, orotate, glycinate, ascorbate and citrate.
Some of these forms are powerful laxatives. The cheaper tablets tend to use the compounds that are more likely to cause laxative effects.
From my research, the general consensus seems to be that chelated magnesium bisglycinate is probably the best, more easily absorbed type.
Unless you're very low, you probably won't notice any sudden, huge changes like I did. You'll just start feeling calmer, more relaxed, less stressed over time.

If you wonder why you haven't seen any of these symptoms mentioned on supplement packaging, it's because (in the UK at least, and presumably in other countries too) there are strict regulation about the claims allowed to be made on food supplements. This is why you get the very bland "Magnesium contributes to a reduction of tiredness and fatigue" or "Magnesium contributes to normal psychological function" type of claims.

Disclaimer

Finally (and I shouldn't need to say this) but given the way the world works I will: I'm not a doctor, and I don't know anything about you. Check and double-check everything I have said here for yourself.