A verb for fluid rushing out in small amount

What is a verb to describe fluid rushing out from an opening in small amount?

"Gush out" sounds like in huge amount. "Seeps through" on the other hand lacks the force that brought the fluid out, like with in "gush".

Consider the verbs jet, spray, and stream. For example, “A fine stream of water jetted from the pinhole” implies small amounts of liquid spraying out under high pressure.

Trickle - (of a liquid) flow in a small stream.

Usage: "A solitary tear trickled down her cheek."

OR

Spurt - A sudden short burst, as of energy, activity, or growth.

Usage: "The pus spurted onto the mirror."

For "small amount" use drip:

To fall in drops: Water is dripping from that leaky faucet.

You're right that seep (not sip) implies a passive and slow movement, with no force suggested. If you want a word for "small amounts of water rushing out", I can only think of leak. A leak does not necessarily need high pressure but it can have it:

to let a liquid, gas, light, etc., enter or escape, as through an unintended hole or crack.

If you are referring to a pressurized container with a small hole, I would recommend escaping.

The problem is that if a liquid is rushing out, it is rarely doing so in small quantities.

Dribbling or dripping

Usage: "The water is barely dribbling out of the faucet."