I will advice to go for hauling time ie trawl hauling/ hr. Alternatively it is more advisable to consider trawl mouth open time and depth of operation.

For what concerns the stock assessment, the fishing effort must be defined to be proportional to fishing mortality. Therefore, the time spent in searching for schools of fish can not be considered as fishing effort.

see:

Sparre P., Venema S. C., 1998. Introduction to tropical fish stock assessment. Part 1. Manual. Fao Fisheries Technical Paper.  N° 306.1, Rev. 2. Rome, FAO. 1998. 407p.

Hilborn, R. and C.J. Walters 1992. Quantitative Fisheries Stock Assessment : choice, dynamics and uncertainty. Chapman and Hall, Inc. New York. ISBN 0412022710

REPORT OF THE SCSI/SCSA/SCESS TRANSVERSAL WORKSHOP ON MEASUREMENT AND STANDARDISATION OF FISHING EFFORT Fuengirola (Malaga), Spain, 30–31 May 2006

I think search time is more important, and maybe the best unit of effort as the set time maybe very short and catch really high as in Purse seine fisheries. However, clearly defining search time is important.

 should take into account that fishing trips are long, and searching for a shoal

Time spent in searching for fish shoal is more important

Times trip and swept area of mouth trawl is important and can use to define the real effort.

CPUE per day or CPUE per boat trip will give good results