gotear

verb
  1. To drip or leak slowly in small drops. verb
    The faucet started to gotear, leaving a small puddle on the sink.
    After the rain, the roof began to gotear, indicating a need for repairs.
  2. To ooze or trickle slowly, often used metaphorically. verb
    Her confidence seemed to gotear away with each passing day.
    The excitement of the event began to gotear as the night wore on.