Makefile - run time decisions using ifeq - makefile

Question

I am trying to solve a particular problem where variables are assigned in one recipe and then interpreted in other recipes, all during run time. As I understand it, ifeq conditions are evaluated during parsing which doesn't work for me as some of them are always false. Is there a way to implement what I'm trying to do (expected output is below)? I'll provide more info if needed.
I'm using make version 3.81 on Linux Mint 17.1.
Here is what I have so far:
fourth =
all: check valueOfFourth definitionOfFourth
.PHONY: all
check:
#echo "TEST"$(cnt)
ifeq ($(first),$(second))
#echo "1. First condition"
$(eval fourth = "first")
else ifeq ($(first),$(third))
#echo "1. Second condition"
$(eval fourth = "second")
else
#echo "1. Conditions weren't met"
endif
valueOfFourth:
ifeq ($(fourth),"first")
#echo "2. First"
else ifeq ($(fourth),"second")
#echo "2. Second"
else
#echo "2."
endif
definitionOfFourth:
ifeq ($(fourth),)
#echo "3. Variable is not defined"
else
#echo "3. Variable is defined"
endif
It is invoked like this:
make cnt="1" first="x" second="x" third="y" && printf "\n" && \
make cnt="2" first="x" second="y" third="x" && printf "\n" && \
make cnt="3" first="x" second="y" third="z"
Expected output:
TEST1
1. First condition
2. First
3. Variable is defined
TEST2
1. Second condition
2. Second
3. Variable is defined
TEST3
1. Conditions weren't met
2.
3. Variable is not defined
Actual output:
TEST1
1. First condition
2.
3. Variable is not defined
TEST2
1. Second condition
2.
3. Variable is not defined
TEST3
1. Conditions weren't met
2.
3. Variable is not defined
It is evident that only the "check" target does what it is supposed to do, the other two simply do not work.

Answer 1

I'm still not entirely clear how these targets are supposed to interact (any interaction between them is generally a bad idea as parallel make execution means that without being explicitly sequenced via prerequisites between them execution order is not guaranteed). But assuming non-parallel make and that each target is supposed to output one of the lines of output I believe this does what you want.
.PHONY: all
all: check valueOfFourth definitionOfFourth
ifeq ($(first),$(second))
fourth = First
condmsg = $(fourth) condition
else ifeq ($(first),$(third))
fourth = Second
condmsg = $(fourth) condition
else
condmsg = Conditions weren'\''t met
endif
check:
#echo 'TEST$(cnt)'
#echo '1. $(condmsg)'
valueOfFourth:
#echo '2. $(fourth)'
definitionOfFourth:
ifeq ($(fourth),)
#echo "3. Variable is not defined"
else
#echo "3. Variable is defined"
endif