It's hard, made me think a little. Here's how you can do it:
You need to set the x axis format to %H:%M, and then replace with 00:00dates similar to those made in this answer .
, . stats (, , 4.6.0), , strptime :
fmt = "%Y-%m-%d|%H:%M:%S"
stats 'file.txt' using (strptime(fmt, stringcolumn(1))) nooutput
t = int(STATS_min)
t_start = t - tm_hour(t)*60*60 - tm_min(t)*60 - tm_sec(t)
num_days = 2 + (int(STATS_max) - t)/(24*60*60)
set xdata time
set timefmt fmt
set xtics 4*60*60
set for [i=1:num_days] xtics add (strftime('%m/%d', t_start+(i-1)*24*60*60) t_start+(i-1)*24*60*60)
set format x '%H:%M'
plot 'file.txt' using 1:2 with lines
num_days 2, x- .
( 4.6.4):
