Issue with cron – Connection Refused

I’m using an external trigger for /path/to/my/website/wp-cron.php. This is managed by my webhost, and I have no clue as to how it works under the hood (though I suspect some implementation of a crontab, since I need to provide a filesystem path to the wp-cron.php file).

The Object Cache plugin works OK in the website itself.

However, when running via the trigger, I get:

RedisException: Connection refused in /path/to/my/website/wp-content/object-cache.php:631
Stack trace:
#0 /path/to/my/website/wp-content/object-cache.php(631): Redis->connect('127.0.0.1', '6379', 1, NULL, NULL, 1)
#1 /path/to/my/website/wp-content/object-cache.php(480): WP_Object_Cache->connect_using_phpredis(Array)
#2 /path/to/my/website/wp-content/object-cache.php(173): WP_Object_Cache->__construct(true)
#3 /path/to/my/website/wp-includes/load.php(701): wp_cache_init()
#4 /path/to/my/website/wp-settings.php(131): wp_start_object_cache()
...

I stress again: the plugin works when viewing the website directly.

Please advise.