According to this post and also here using a variable for the upstream server like this:

location /git/ {
  resolver 127.0.0.11 ipv6=off valid=30s; ## internal docker dns set 
  $upstream http://gitea:3000/;
  proxy_pass $upstream;
}

allows nginx to start even when the upstream service isn't available.

However having tried this all the requests to /git/ return the document root.

Here's a gotcha.

Here's a solution.

location /git/ {
  resolver 127.0.0.11 ipv6=off valid=30s; ## internal docker dns set 
  $upstream http://gitea:3000/$uri$is_args$args;
  proxy_pass $upstream;
}

However this means that root level requests like https://sigyl.com/git/giles 404

Configure logging of proxy passes in the log_format directive:

http {
    include       /etc/nginx/mime.types;
    default_type  application/octet-stream;

    log_format  main  '$remote_addr - $remote_user [$time_local] "$request" '
                      '$status $body_bytes_sent "$http_referer" '
                      '"$http_user_agent" "$http_x_forwarded_for"'
                      '"$proxy_host" "$upstream_addr"';

looking at the gitea logs - these requests are 404ing because the /git/ at the start is included:‌‌

[Macaron] 2020-05-03 08:27:59: Completed GET //git/ 404 Not Found in 1.997719ms
[Macaron] 2020-05-03 08:27:59: Started GET //git/img/404.png for 10.0.11.4
[Macaron] 2020-05-03 08:27:59: Completed GET //git/img/404.png 404 Not Found in 2.133087ms
[Macaron] 2020-05-03 08:28:02: Started GET //git/serviceworker.js for 10.0.11.4
[Macaron] 2020-05-03 08:28:02: Completed GET //git/serviceworker.js 404 Not Found in 1.998517m

This post talks about how to remove the location from the uri.

I ended up using a regex like this:‌

location ~ /git/(.*) {
  resolver 127.0.0.11 ipv6=off valid=30s; ## internal docker dns set
  $upstream http://gitea:3000/$1$is_args$args;
  proxy_pass $upstream;
}

Now if I stop gitea service  and restart the proxy:

docker service scale gitea_gitea=0
docker kill ef791407a0ac

it stays up.