What can go wrong for LiveQuery when start using HTTPS (indeed it was nginx)?

On local and stage servers with HTTP LiveQuery work fine. But on prod server don’t work functionality based on it and I don’t see some lines in logs that point LiveQuery is working.
When the first client after start connect on HTTP I could see:

    info: Parse LiveQuery Server starts running

    info: Create new client: xxx-xxx-....

On prod (HTTPS) only

    info: Parse LiveQuery Server starts running

No info about connect, nor about disconnect.

Use only 2 settings for LiveQuery

"liveQuery": {
    "classNames": ["xxx", "xxx", "xxx"]
 "startLiveQueryServer": "true"

and both are the same for all servers.

I don’t think that something with parse server, rather outer reasons, but what it could be?..

UPD. When try to connect via LiveQueryClient I have got error:

e =  Event {
  "isTrusted": false,
  "message": "Expected HTTP 101 response but was '403 Forbidden'",

UPD2. I was advised to read this, becouse our server use nginx.

In the end it turned out that does not matter - HTTP or HTTPS - the new impotant element become nginx. Changing protocol to HTTPS was just a coincidence. Everything had to be revealed on stage server but there still simple setup without proxy.

All was solved by adding two lines to nginx config:

    proxy_set_header Upgrade $http_upgrade;
    proxy_set_header Connection "upgrade";

in according with abovementioned manual or analogical article.

But I don’t understand may be the second example from there (more complicated with map section) will be better?