Here's the fix:
obj=vehicle
name=LMS-Mail
speed=160
copyright=Kieron/James
intro_year=1933
intro_month=6
retire_year=1951
retire_month=2
waytype=track
freight=Post
payload=60
length=9
weight=30
cost=510000
runningcost=26
sound=-1
can_lead_from_rear=0
bidirectional=1
loading_time=8500
comfort=0
Constraint[Next][0]=LMS-d1904-Coach
Constraint[Next][1]=LMS-d2007-Parcel-Brake
Constraint[Next][2]=LMS-d1904-Dining
Constraint[Next][3]=LMS-Mail
Constraint[Next][4]=LMS-TPO
EmptyImage[E]=./images/lms-mail.0
EmptyImage[SE]=./images/lms-mail.1
EmptyImage=./images/lms-mail.2
EmptyImage[SW]=./images/lms-mail.3
EmptyImage[W]=./images/lms-mail.4
EmptyImage[NW]=./images/lms-mail.5
EmptyImage[N]=./images/lms-mail.6
EmptyImage[NE]=./images/lms-mail.7
---------------------------------
obj=vehicle
name=LMS-TPO
speed=160
copyright=Kieron/James
intro_year=1933
intro_month=6
retire_year=1951
retire_month=2
waytype=track
freight=Post
payload=40
length=9
weight=30
cost=720000
runningcost=37
sound=-1
can_lead_from_rear=0
bidirectional=1
catering_level=1
loading_time=8500
comfort=0
increase_maintenance_after_years=15
years_before_maintenance_max_reached=30
# Wooden bodied vehicles become obsolete sooner.
Constraint[Next][0]=LMS-d1904-Coach
Constraint[Next][1]=LMS-d2007-Parcel-Brake
Constraint[Next][2]=LMS-d1904-Dining
Constraint[Next][3]=LMS-Mail
Constraint[Next][4]=LMS-TPO
EmptyImage[E]=./images/lms-tpo.0
EmptyImage[SE]=./images/lms-tpo.1
EmptyImage=./images/lms-tpo.2
EmptyImage[SW]=./images/lms-tpo.3
EmptyImage[W]=./images/lms-tpo.4
EmptyImage[NW]=./images/lms-tpo.5
EmptyImage[N]=./images/lms-tpo.6
EmptyImage[NE]=./images/lms-tpo.7
The bolded parts are the changed parts. Some of this file has been changed for Experimental purposes, but copying and pasting the constraints part alone should fix the issue. (Previously, the figure 0 had been used for most of the constraints, rather than an ascending series of numbers).
