Theme -- I can't do much better than the unifier, so let's start with that.
56 A. Relatively unknown quality items ... and what can be found in 16-, 26- and 42-Across: HIDDEN GEMS. Typically something great that most people don't know about. Here, it's literally precious stones hidden in the theme fill.
16 A. Arose to catch the proverbial worm: GOT UP EARLY. Arise before dawn - or, in my case, before 9:00 a.m. Do that that and you might be able to catch an oyster with a perfect PEARL. This is a small, spherical, usually white object that forms around a grain of sand inside the shellfish. Pearls are commonly strung together as a necklace.
5. On: ATOP.
9. Arthur of tennis: ASHE.
13. Country quarters: INNS. Establishments for the lodging and entertainment of travelers, generally smaller than hotels and with fewer amenities.
14. Be behind: TRAIL. Lag
15. Skier's need, maybe: SNOW. For several varieties of down-hill or cross-country skiing
18. Presidents' Day event: SALE. Many holidays really.
19. Ivy League student: ELI. Specifically at Yale U.
20. Dynamic prefix: AERO. Designed to reduce air drag and/or wind resistance.
21. Sushi bar brews: SAKES. A fermented rice beverage
22. Ristorante favorite: LASAGNA. Layers of noodles, meat and cheese, usually with a tomato based sauce.
24. "Holy smokes!": ZOWIE. Golly!
30. Monks' wear: COWLS. Long, hooded garments with wide sleeves, sometimes, just the hood.
33. Total drubbing: ROUT. Like a bad Super Bowl game.
34. Flatow of "Science Friday": IRA. [b. 1949] A radio and television journalist and author.
35. Opposite of home: AWAY.
36. Dozen dozen: GROSS. That's 144 of anything.
38. Craftsy etailer: ETSY. An American e-commerce website focused on handmade or vintage items and craft supplies.
39. Tiny, for short: LI'L. Little, for long
40. "Not long": SOON. Li'l bit of time.
41. Guilty and not guilty: PLEAS. Formal statements by or on behalf of a defendant or prisoner, stating guilt or innocence in response to a charge, offering an allegation of fact, or claiming that a point of law should apply.
46. Spectrum maker: PRISM. Could be a brand name product or service, but not this time. A PRISM will divide white light into color components, based on wave length.
47. Comment after a missed shot: NICE TRY. Condolence or sarcasm?
51. Characteristic: TRAIT. A distinguishing quality of a person or thing.
53. Shred: IOTA. Tiny amount
54. Tint: HUE. Coloration
55. "I didn't mean to do that": OOPS. Utterance after an accident.
59. Unmitigated joy: GLEE. Originally, the specific joy of music and singing.
60. Seller, usually: OWNER. Or his/her agent.
61. Its symbol is Fe: IRON. Elemental metal.
62. Some cameras, for short: SLRS. Single Lens Reflex.
63. Amorously pursues: WOOS.
64. Fiddling emperor: NERO. While Rome burns.
Down:
1. Orion's left foot, some say: RIGEL. Rigel is a blue supergiant that is the brightest star in the constellation Orion (the Hunter). Due to its measured size and brightness it is expected to end in a supernova one day.
2. __ Gay: ENOLA. a Boeing B-29 Superfortress bomber, named after Enola Gay Tibbets, the mother of the pilot, Colonel Paul Tibbets. On 6 August 1945, piloted by Tibbets and Robert A. Lewis during the final stages of World War II, it became the first aircraft to drop an atomic bomb.
3. Naysayers: ANTIs. Those with negative viewpoints.
4. Pelican State sch.: LSU. Louisiana State University.
5. Biblical mount: ARARAT. Legendary landing place of Noah's Arc.
6. Tropical root vegetable: TARO. A food staple in African, Oceanic and South Asian cultures.
7. Squeaky-wheel need: OIL. Lubricant.
8. Tissue layer: PLY. A single layer of any multiple layer construction, such as ply wood.
9. Attack: ASSAIL.
10. Hazard in many old Westerns: SNAKE BITE.
11. Opening: HOLE. An aperture or gap.
12. Lambs' moms: EWES. Female sheep.
14. New drivers, typically: TEENS. People between the ages of 13 and 19, inclusive.
17. Novel units: PAGES. Not new and unusual things, but the two-sided papers bound into books.
21. Whack at a mosquito: SWAT.
23. With skill: ABLY.
24. Family outing destinations: ZOOS.
25. Numbered piece: OPUS. A separate composition or set of compositions by a particular composer, usually ordered by date of publication.
27. Outlet insert: PRONG. A slender pointed or projecting part: such as a fang of a tooth ora point of an antler, or an electric plug.
29. First Black MLB team captain, 1964: MAYS. Willie Howard Mays Jr., [b 1931] nicknamed "The Say Hey Kid", is an American former professional baseball center fielder. He spent almost all of his 22-season Major League Baseball career playing for the New York/San Francisco Giants before finishing his career with the New York Mets. [Wikipedia]
30. Not nervous: CALM. Serene.
31. Something Mommy needs to kiss?: OWIE. Booboo.
32. Computer screen background: WALLPAPER.
36. Odin and Thor: GODS. In the Aesir.
37. Wander: ROAM.
38. "Need anything __?": ELSE.
40. Sulky state: SNIT.
41. Pie nut: PECAN.
43. Flowery van Gogh work: IRISES. You can see it here.
44. Battery terminals: ANODES. And Cathodes
45. Solution strength measure: TITER. Determined by 2 conflicting methods. Read about it here.
48. "Over __!": THERE. A 1917 song written by George M. Cohan that was popular with the United States military and public during both world wars. It is a patriotic song designed to galvanize American young men to enlist and fight.
50. Type of survey question: YES/NO. As opposed to multiple guess.
51. Duds: TOGS. Clothing.
52. Dinner table staple: ROLL. A small, usually round or oblong individual loaf of bread served as a meal accompaniment (eaten plain or with butter)
53. License plate fig.: ID NO. Identification Number.
56. "__ come?": HOW. Said when asking how or why something happened or is the case.
57. Iconic WWII island, briefly: IWO. An island 750 miles south of Tokyo. It was the site of an iconic WW II battle in February and March of 1945.
58. Winning game cry: GIN. From a card game, not a martini, alas.
Cool Regards!