A period of time as in the colloquial American English, Come sit a spell. I hear it mostly from the mouths of rural Americans in the movies. Does that reflect general usage? OED tells us this:

spell, n.3

1. A set of persons taking a turn of work in order to relieve others; a relay, relief-gang, or shift. Now rare.

1593 Sir F. Drake Revived (1628) 27 Rowing in the eddy..by spels, without ceasing, each company their halfe houre glasse.

3. b. dial. and Austral. An interval or period of repose or relaxation; a rest.

Examples from 1863 to 1975 may be found in Dict. Newfoundland Eng. (1982).

c1845 J. Tucker Ralph Rashleigh (1929) xi. 146 Both men took a hoe and gave the children a spell.
1847 J. O. Halliwell Dict. Archaic & Provinc. Words II Spell,..pleasure; relaxation. Somerset.
1852 G. C. Mundy Our Antipodes I. xi. 363 Your carriage horses will be all the better for a ‘spell’, (a rest).

For the etymology OED says “Related to spell v.3, and perhaps directly representing Old English gespelia substitute (compare spala spale n.1).” Spale, an obsolete word meaning sparing, respite or rest has only one cite in the dic, from the wonderful old poem The Owl and the Nightingale.

a1250 Owl & Nightingale 258 Þu mihtest bet hote galegale, Vor þu hauest to monye tale. Let þine tunge habbe spale.

Gespelia is interesting, I wonder if there are any other cognates in English of this OE term.

There is a lot more in the OED entry. I would say that it’s not generally used in American English, but is, as you surmise, considered a rural, regional term. But you do see it in particular constructions, a spell of X weather or doing a spell in prison.

It can also be a verb as in “Hey, let me spell you a while”, meaning to give someone a break and take over a (usually) physically tasking or tedious activity for a short period. It’s less common now than a few decades ago, but probably unremarkable and understood by most. Quite common among the twenty-somethings at my last job where manual labor was often required.

My experience is completely different. (Showing the problems with anecdotes.) In 2009 I was in a class with a bunch of 20-something grad students. The professor, in her late 40s like me, used spell as a verb, and I was the only one who comprehended what she said.

I’m more familiar with the common verb usage: “To charm, fascinate, bewitch...” as in to put a spell on me, and Spellbound, which is the title of one of Hitchcock’s famous films.

I’ve never heard anyone use the verb to spell in this way. Yes, I know it’s in the dictionaries, but I dispute that it is in any way common. To put a spell on someone and spellbound are not uses of this verb.

To put a spell on someone and spellbound are not uses of this verb.

Correct, but I was just more familiar with these usages.

I’ve heard the verb spell used in regard to horses, or more rarely human sportspeople. I would consider it a somewhat old-fashioned and/or very specific to the profession.

A couple of examples from the wild:

https://www.horseyard.com.au/forum/9-horse-training/484-to-spell-a-pony-or-not-to-spell-your-views-please
I think it is a good idea to spell your pony for a short period

http://www.espn.com.au/cricket/story/_/id/21346333/australia-ashes-pace-attack-revealed
Following the match, Hazlewood was involved in discussions with coaches, selectors and medical staff, leading to the decision to spell him from the next Shield match

It’s always dangerous to try to be definitive, but I’m pretty certain the verbal usage, meaning “rest”, is not to be found in BrE, even in horseracing/sport.