From the sun! Never thought I'd ever say this. Every time the sun appears in Northern England, half the male population go shirtless, and that includes me. But the good ole Neighbourhood Quack has had cause to give me advice.
Now, a sunhat doesn't effectively cover the back o the neck, though a sombrero might. Riding a bike with a sombrero ain't gonna win any races, nor will the hat remain in its designated position.
So, short of becoming an aged rocker, or an arab, what would you do?

Me, I'd do nothing. I'm way to old to care.

What I've done for decades in TX: wear a traditional SS cycling jersey which has a collar to protect the nape and SPF 30 sunscreen on exposed epidermis.

-Bandera

https://www.amazon.com/s/ref=nb_sb_n...and+back+flaps

Da Brim

Pony-tail, or is that the "aged rocker" option?

Sometimes I wear a baseball cap, backwards. That works best if you aren't hung up on wearing helmets.

Oh, oh, oh!!! I've got an answer that works.

Check out my avatar and maybe you can figure it out.

I'd rather have skin cancer than wear that thing...

I use Trader Joe's SPF 50+ (spray). It actually tested as labeled by Consumer's Reports.

HAIR???

I saw someone with a brim like that a few days ago. It looked nice.

However, I've removed my visor... I liked the shade, but my head position on the drop bars, I was losing the top of my visual field.

You might try what the construction crews wear. Not sure how it actually attaches to the hard hat, but it could probably be retrofitted for a helmet.

ERB 19281 S268 Mesh Neck Shield - Hi Viz Lime - AboloxSafety.com

I wear one of these:

https://www.amazon.com/gp/product/B0...?ie=UTF8&psc=1

Well, that works great for my ears and back, but how about all those places that no longer have any?

Bandana folded into a triangle and tied at the front around the neck. An alternative with a large enough one is to wear it the traditional way on your head, and the tails from where it is tied will help cover the neck. I adopt the latter method with most of my riding and haven't had neck sunburn, but when off the bike I've used the first method with great effect when wearing T-shirts.

In high summer, you could also look at a good quality, lightweight cotton business shirt so the collar can be turned up. Helps with the cool factor as your sweat evaporates.

Ride at the crack of dawn.

That's what I'm thinking. I'm having difficulty thinking about sunburn on neck. Between the helmet, hair in back, and the top of a jersey, I never worried about burn there.

My wife wears a Sol Skin Skully Cap Voler I believe, works very nice
R

Skull cap modeled after the French Legionaires hat, also saves your ears from the sun.

Thanks guys! I like the bandana idea. Now I gotta look for a jazzy one. . .that doesn't make me look like Keith . . .

I wear stuff like these. Doo rags

https://www.google.com/search?q=due+...cycle+doo+rags

Da Brim:

Ride backwards?

I wear a Mullet

I usually wear bandannas with a long tail, but I'm leaning toward a desert classic in red for the really hot sunny summer days.

For safety, you should also carry a bunch of road flares attached to a MOLLE vest, and maybe a big alarm clock.