This puzzle is part of the Monthly Topic Challenge #4: Cross-*non*-words
Are you getting tired of regular crosswords? If so, then allow me to bring this one to your attention!
Solve the clues and fill the light grey-coloured squares – part of your task is to work out exactly how you're supposed to do that whilst satisfying this month's Topic Challenge criteria (see the linked meta-post above for more information)...
Across:
1. )3( tnegA
3. "I'll return shortly" (3, inits)
4. Acoustic unit of measurement (3)
6. 104 (3)
7. )3( tnuP fo dnaL tneicna eht fo neeuQ
9. 1956 UN convention relating to transportation of cargo by road (3, inits)
11. )stini ,3( dleifraG drahciR yb detaerc emag drac elbitcelloC
13. )3( !fooW
17. Metal food container, prison, or toilet? (3)
18. )stini ,3( "mocimaF" eht sa nwonk osla elosnoc emag oediv emoh tib-8
19. )3( etomiT ni regetni dnoces ro ,nuonorpoeNDown:
1. Provide with weapons (3)
2. )3( tsepaduB ni esuoH arepO etatS nairagnuH eht fo tcetihcrA
3. "It is" in Latin (3)
5. Former UK trade union for academic staff, merged with NATFHE in 2005 (3, inits)
7. Talk continuously and eagerly (3)
8. Political party in Myanmar, in government 2015-2021 (3, inits)
9. )3( reflog lanoisseforp 1 rebmuN dlrow remrof ,___ einrE
10. Common childhood vaccine (3, inits)
12. )3( noiger eniltsaoc nainrofilaC cinecs ,___ giB
14. )stini ,3( ledom ruoloc evitiddA
15. Isotope notation standard (3, inits)
16. Düsseldorf-based leisure airline acquired by Air Berlin in 2007 (3, inits)