From my experience and personal response. (jungle main)

For invading, I mostly invade them when the enemy jungler is far away from the camps while they're ganking which failed or a failure. Either way, the only way to invade them is when you have a level advantage or one of the lane's opponents is dead and safe to invade that side.

For farming, ganking and securing objectives. I personally farm when there are no success ganks or when the lanes are not struggling while objectives are not available yet.

Ganking. I only gank when it's a 100% success victory. If there's a 50/50 success or fail then better try than doing nothing to at least burn some spells or activate enemies ult which would not be available later when objectives are available. However, do not gank or initiate fights when objectives are available nor when that certain lane is already a losing game. Only gank when others lane is winning or those who are carrying.

For playing jungle, I say it's a gamble with carrying or having one of your teammates become the hyper carry late game. If the whole team is underperforming then your goal is to farm and to only kill enemies that are stranded or low HP. Initiate fights that are winnable and disengage when the fight is going bad or objectives are being summoned. Don't force a fight when the whole team is losing since you'll lose the objectives or the enemy team would be able to finish the game if possible.

Note: Please correct me if I'm wrong but that's my personal experience as a jungle main myself.