GTM sending data to VIP IP which is down.

The VIP will always reply to icmp. By default icmp is enabled for every VIP in the LTM. Use basic tcp_half_open to monitor if you do not have Iquery setup. Try something like below,

create gtm server 1.1.1.1 datacenter "INDIA" monitor tcp_half_open addresses add { 1.1.1.1 } product generic-host virtual-servers add { 1_1_1_1_80 { destination 1.1.1.1:80 monitor tcp_half_open } }
create gtm server 2.2.2.2 datacenter "INDIA" monitor tcp_half_open addresses add { 2.2.2.2 } product generic-host virtual-servers add { 2_2_2_2_80 { destination 2.2.2.2:80 monitor tcp_half_open } }

create gtm pool test_pool load-balancing-mode round-robin verify-member-availability enabled ttl 30 members add { 1.1.1.1:1_1_1_1_80 }
create gtm pool test_pool_2 load-balancing-mode round-robin verify-member-availability enabled ttl 30 members add { 2.2.2.2:2_2_2_2_80 }

create gtm wideip test.wideip.com ipv6-no-error-response enabled pool-lb-mode round-robin pools add { test_pool { order 1 } test_pool_2 { order 0 } }