Can ‘pants’, ‘glasses’, ‘scissors’, et similar in the sense of “a pair of [..]” take singular-number verbs? Why or why not?, Which ones / Which not?
Does this sound wrong to native speakers?
Yes.
If it does, can I do it anyway?
Yes, but many people will think less of your language skills if you do.
I know lots of people who speak English as a second language and have lived and worked in English-language environments for decades. Some of them use incorrect idioms repeatedly. One likes to say "war broke up" instead of "war broke out." Another likes to say "go outside for dinner" instead of "go out for dinner." We all know what they mean, but even after many years it is still odd and disorienting to hear it.
Let me clarify a little further. Look at the words scissors, glasses, pants. Each is a plural. You want to be able to say, "The scissors is over there," but the problem is that you're referring to a plural and therefore can't use "is." You can say, "The scissor is over there, but then you'd be referring to a single one of the two parts that make up a pair of scissors. You could not say "The pants I bought is on the bed," and it would be ridiculous to say, "The pant I bought is on the bed" because we never refer to half of a pair of pants. I don't think the issue is one of tradition, but just basic subject/verb agreement.
Where ❓❓is my glasses? I must have put ❓❓it somewhere around here.
Does this sound wrong to native speakers? If it does, can I do it anyway?
Yes, it sounds wrong, the statement much more so than the question. Yes, you can do it, but the former will sound "incorrect" in an ordinary way typical of fluent speakers' casual speech. The latter will sound glaringly wrong, and something only a non-native speaker will do.
Some dialects of English, at least historically, used singular verb forms with some plural subjects, for instance the stereotypical Westcountry "them's the one, they is". But unless your accent matches, and you exhibit other features of a suitable dialect, nobody's going to think you're talking proper Westcountry.
That feature is probably restricted to basolects in any case.
However, specifically "there is" and "where is" are so frequently reduced to "there's" or "where's" that it's pretty unremarkable, in speech at least, to say things like
Where's the kids?
There's only five eggs in this carton.
If you were to use the uncontracted form, it would sound a little bit more wrong, but not egregiously so.
But using a singular verb form, or indeed a singular pronoun, to refer to something that's grammatically plural, is just not done by native speakers (except in specific dialects as mentioned above):
* The scissors is on the table.
* The scissors? It's on the table.
Unless you finish that sentence with "Mr Frodo sir" or "Professor Iggins", it will most definitely raise eyebrows.
[Added in response to a request by OP]
By way of comparison: every schoolkid's starter geometry set used to include a ruler, a pencil, an eraser, two set squares, a protractor, and a device for drawing a circle. Our teachers would always refer to this device as a pair of compasses (which is indeed the "correct" name). Most of the kids would continue to call it a compass despite the teachers' admonishments. (A compass is a device for pointing north.)
Of course, compass ends with a sibilant, so its plural has a whole extra syllable /ɨz/ at the end, whereas we pluralise scissor by just adding /z/ to the end, without adding an extra syllable. Maybe the fact that a kid can say "my scissors" for almost no more effort than "my scissor", but that "my compasses" is a bit more work than "my compass", contributes to the way that pair of compasses often gets entirely de-pluralised, while pair of scissors rarely does. (Notwithstanding @MichaelHarvey's interesting points about a scissor being idiomatic Welsh!)